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Vol. 8. Issue 5.
Pages 4894-4914 (September - October 2019)
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Vol. 8. Issue 5.
Pages 4894-4914 (September - October 2019)
Review Article
DOI: 10.1016/j.jmrt.2019.06.014
Open Access
A critical review of experimental aspects in ratcheting fatigue: microstructure to specimen to component
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Surajit Kumar Paul
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surajit@iitp.ac.in

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Department of Mechanical Engineering, Indian Institute of Technology Patna, Bihta, Bihar 801106, India
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Abstract

In the past three decades ratcheting fatigue has attracted lots of research interest. Ratcheting can be defined as the directional progressive accumulation of plastic deformation of a material when it is subjected to a primary load along with a secondary cyclic load. The current article addresses the recent progresses made on the experimental front on the ratcheting behavior spanning from the specimen level to the component level and its correlation with microstructural evolution. The experimental aspects of ratcheting include the effect of stress levels, stress rate, temperature, planar anisotropy, previous loading history, and multiaxial loading paths. This work also discusses two test controlling modes engineering and true stress control ratcheting and their comparison, ratcheting-tensile, ratcheting-low cycle fatigue, ratcheting-ratcheting, ratcheting-creep interactions and ratcheting in component level. This summarized information clarifies why ratcheting is presently an important topic of engineering research.

Keywords:
Uniaxial and multiaxial ratcheting
Non-proportional loading
Mean stress dependent hardening
True stress control test
Ratcheting damage
Ratcheting interactions
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1Introduction

Cyclic plastic deformation in structures and engineering components is the major source of fatigue life limiting factor in the critical engineering installations. It is not essential that the entire structure or component experiences plastic deformation during load reversal. Local stress concentrators like inclusions and defects, material inhomogeneity, geometrical discontinuities, surface roughness, scratches, joints corner, welding defects, etc. may be the cause of local cyclic plastic deformation. Once early fatigue cracks are initiated from the locally cyclic plastic deformed region, it will grow and contribute to premature failure of the components. Different forms of cyclic plastic deformation can be observed in engineering materials, for example low cycle fatigue (LCF), ratcheting, and mean stress relaxation as summarized in Fig. 1. LCF normally takes place during symmetric strain cycling, mean stress relaxation occurs during asymmetric strain cycling, and ratcheting happens due to asymmetric stress cycling. For LCF, mean stress relaxation and ratcheting, the necessary condition is that the deformation should be in the plastic domain. Among different forms of cyclic plastic deformation, ratcheting has the highest detrimental effect on fatigue life. Taking into account the significance of ratcheting in the structural integrity of components, extensive research activity has been carried out by several researchers to understand this ratcheting phenomenon in the last three decades. As shown in Fig. 2, a significant boost in research work dedicated to ratcheting has observed particularly in the last three decades. The growth in the number of technical article in the field of ratcheting evidently points out a growing engineering and academic interest. Thus it is a right instant to plan a complete evaluation of the recent progress achieved for the mechanism of ratcheting response in the microscopic scale, macroscopic ratcheting response at different loading conditions, and finally overall ratcheting performance of components or structures.

Fig. 1.

Different types of cyclic loading and corresponding material response.

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Fig. 2.

Evolution of the number of publications related to ratcheting for the last 28 years. Data extracted with Google scholar (http://scholar.google.com/advanced_scholar_search). Search done by key words: ratcheting, ratchetting and cyclic creep.

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Ratcheting can be classified as (i) material ratcheting and (ii) structural ratcheting. Material ratcheting can be visible in the absence of structural effects (i.e., in a structure if stress is homogeneously distributed), thus material ratcheting can be investigated by material experiments and the material ratcheting can be expressed by constitutive equations. Hübel [1] has explained the structural ratcheting. Structural ratcheting can takes place due to inhomogeneous multiaxial stress state arises from various load combinations and inelastic material response in cyclic loading. An example of structural ratcheting can be described as a simple straight pipe which is in a fixed internal pressure and experiences cyclic thermal gradient in the radial direction. For this example, primary load arises in the circumferential and axial directions because of steady internal pressure, while secondary load (i.e., cyclic bending moment) arises from the cyclic thermal gradient. Finally, the structural ratcheting takes place until the plastic collapse of the structure if the loads are sufficient to deform the structure plastically. The structural ratcheting can be verified from the detailed inelastic analysis.

Material ratcheting is a secondary deformation process that accumulates progressively with number of cycles, and is responsible to severely deteriorate the performance of a component due to the cumulative effect of directional progressive plastic strain accumulation and fatigue damage. Considering the fact that asymmetric stress cycling (i.e., cyclic stressing with non-zero mean stress) may be experienced in engineering components/structures. Consideration of ratcheting phenomena is extremely essential and should be considered in the design, remaining life estimation, and safety assessment of such components/structures. For examples: ratcheting causes significant amount of plastic deformation in the piping component like ovalization of elbows and T-joints in cyclic bending, local cross-sectional area reduction and local bulging of pipes under constant internal pressure and cyclic loading, etc. [2,3]; in the front of the crack tip within the reverse plastic zone the material undergoes ratcheting deformation [4]; at the transverse rib root of Thermo-Mechanically Treated (TMT) rebar deformed through ratcheting during cyclic plastic deformation [5,6]. Seeing the importance of ratcheting, similar to fatigue and creep damage mechanisms, ratcheting is also included in various design criteria for engineering structures and components, including ASME Code Section III [7], EN13445 [8], KTA [9], R5 [10] and RCC-MR [11]. According to these criteria, the structures should be designed under the ratcheting domain where only elastic or plastic shakedown takes place [12]. Three possible types of ratcheting behavior exist for a material, these are (i) decreasing ratcheting strain rate leading to elastic/plastic shakedown where no additional ratcheting strain accumulation is noticed. This type of response is normally visible in severely cyclic hardened materials. Elastic shakedown causes high cycle fatigue (HCF) and plastic shakedown results LCF in the material after initial ratcheting. (ii) Constant ratcheting strain rate leading to continuous accumulation of ratcheting strain. In this process the material fails by fatigue crack initiation and propagation. And (iii) increasing ratcheting strain rate leads to large accumulation of ratcheting strain, which causes plastic instability and necking (Fig. 3). The number of cycles to failure is very low for increasing ratcheting strain rate. Generally, severely cyclic softened materials or at high mean stress and stress amplitude combination loading condition shows this type of ratcheting response. The specimen elongates with the number of cycles due to the progressive buildup of plastic strain. This progressive elongation of the specimen results reduction in cross sectional area and finally leads to overload failure (i.e., ductile or brittle depending upon material and loading condition) of the specimen due to plastic instability/necking.

Fig. 3.

Three possible types of ratcheting behavior.

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It is helpful to recap the history of ratcheting fatigue research, before in-depth review work. Investigation on ratcheting has reported by Bairstow [13] in 1911. He has presented strain accumulation under cyclic uniaxial stressing with tensile mean stress in a steel sample. Axial strain progression due to asymmetric uniaxial loading has also been reported by number of investigators at high temperature by Lazan [14], Manjoine [15], Kennedy [16], Meleka and Evershed [17]; at room temperature by Benham and Ford [18], Coffin [19]; at low temperature by Moyar [20], Moyar and Sinclair [21]; wood and Bendler [22]. Coffin [23] on 1964 has observed shifting of stress-strain hysteresis loop during cyclic deformation experimentation with mean stress on 1100 aluminum. Latter Benham [24] on 1965 has conducted an extensive cyclic creep/ratcheting research on Mild steel. He has reported that the rate of ratcheting is dependent on the strain hardening or softening behavior of the material. He also observes two types of fracture; one is failure by fatigue crack propagation and another by gross plastic deformation. Radhakrishnan [25] in 1975 has conducted multiaxial ratcheting experiment on aluminum and steel. He has noticed that an alternating twist of ±θ between two successive tensile stressing increases the plastic strain on the next reloading. After that a considerable number of research work, done on various aspect of ratcheting on different materials and the literature is used to review the ratcheting fatigue in details and section wise in this present review article.

2Progress in specimen level experimental observation

Investigation on ratcheting is essential where load excursion is not symmetric in nature. Two cumulative damage effects in ratcheting (fatigue damage by formation of stress-strain hysteresis loop and accumulation of ratcheting strain) can deteriorate the performance of a component. Stress cycling with tensile mean stress, results ratcheting strain accumulation in the tensile direction as well as thinning out of the components cross-sectional area and their join consequence, can lead to premature failure of the specimen [26–29]. A schematic block diagram as shown in Fig. 4, illustrates the evolution of ratcheting damage. Loading conditions, i.e. stress amplitude, mean stress and prior loading history have an immense effect in ratcheting damage. The center position of the stress-strain hysteresis loop along the strain axis denotes the ratcheting strain. The geometric mean of peak and valley strain of a cycle can be considered as ratcheting strain. Mathematically the axial ratcheting strain εr can be expressed as:

where εmax and εmin are the maximum and minimum axial strains respectively for a particular cycle.

Fig. 4.

Schematic representation of ratcheting damage.

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The typical evolution of ratcheting strain with number of cycles has been shown in Fig. 5(a) for SA333 CMn steel. A typical ratcheting curve can be divided into three regions: primary, secondary and tertiary regions. The nature of the ratcheting curve is comparable to a traditional creep curve, although the deformation and damage mechanisms are vastly different. Movement of dislocations, their interaction and cell formation are associated with ratcheting [30,31], while creep is connected with diffusion controlled glide and climb of dislocations, grain boundary sliding and void formation [32]. Two competitive mechanisms geometrical softening and cyclic hardening are operative in engineering stress/load control ratcheting experiments [33]. In the primary region, cyclic hardening dominates [34] because the reduction in cross sectional area is less. Therefore, ratcheting rate decay in the primary region is mostly because of cyclic hardening of the material [35]. The balance effect of cyclic hardening and cross sectional area reduction are associated with steady ratcheting strain accumulation rate in the secondary region. In the tertiary region, cross sectional area reduction is substantial because of high ratcheting strain accumulation and hence softening dominates [28,36]. This reduction of cross sectional area of the specimen results in enhancement of maximum true stress and finally necking. The three distinct regions of ratcheting also can be distinguished from ratcheting strain rate versus number of cycles plot, which is illustrated in Fig. 5(b) for SA333 CMn steel. For low amount of ratcheting strain accumulation, the tertiary region of ratcheting curve is observed after initiation of the fatigue crack.

Fig. 5.

Ratcheting at stress amplitude of 310 MPa and mean stress of 80 MPa (a) Ratcheting curve with three distinct zones [34] (b) Ratcheting rate curve with three distinct zones [34].

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The variables that influence the material’s ratcheting response are discussed in the following sub-sections.

2.1Effect on applied stress level

Applied stress levels have an immense effect on ratcheting strain evolution. Applied stress levels can be defined by (i) mean stress and stress amplitude, (ii) Maximum stress and stress ratio (R = ratio of minimum stress and maximum stress) and (iii) Minimum and maximum peak stress of a cycle. Any of these three can reveal the same result. In this work, mean stress and stress amplitude based investigations are discussed.

2.1.1Effects of stress amplitude on uniaxial ratcheting behaviors

Directional cyclic strain buildup in asymmetric stress cycling is completely depending upon the applied stress level in absence of other factors. Irrespective of material and stress rate, different researchers are found the same conclusion that the ratcheting life declines and ratcheting strain accumulation rate enhances with increase in stress amplitude at constant mean stress. Paul et al. [28,36] for SA333 steel, Paul et al. [28,37] for 304 L N, Lin et al. [38] for hot-rolled AZ31B magnesium alloy, Lin et al. [39] for hot-rolled AZ91D magnesium alloy, Lim et al. [40] for Cu alloy, Dutta and Ray [41] on IF steel, Dutta and Ray [42] on 304 L N, and many more have found the same observation. Fig. 6 shows the effect of stress amplitude on uniaxial ratcheting performance of SA333 CMn steel under mean stress of 80 MPa and stress rate of 50 MPa/s. The ratcheting life decreases with increasing stress amplitude at constant mean stress. Among the three stages of ratcheting, as discussed in Fig. 5(a), the ratcheting strain rates are calculated from the secondary stage for all ratcheting curves. The ratcheting strain rate changes significantly with the variation of the stress amplitude (Fig. 6(b)).

Fig. 6.

Uniaxial ratcheting tests with the constant mean stress of 80 MPa and stress rate of 50 MPa/s for SA333 CMn steel: (a) ratcheting strain evolution with number of cycles [34]; (b) ratcheting strain rate evolution [34].

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2.1.2Effects of mean stress on uniaxial ratcheting behaviors

In this sub-section, the sensitivity of uniaxial ratcheting response with the mean stress for the SA333 CMn steel is discussed. Fig. 7 illustrates that the mean stress has an immense effect on the uniaxial ratcheting strain accumulation of the SA333 CMn steel. Obviously, the rise of mean stress results in the fast enhancement of the uniaxial ratcheting strain accumulation and the decrease in ratcheting life. Moreover, both the increase of ratcheting strain accumulation rate and reduction of ratcheting life are few folds when the mean stress is moved up from 40 to 120 MPa.

Fig. 7.

Uniaxial ratcheting tests with the constant stress amplitude of 310 MPa and stress rate of 50 MPa/s for SA333 CMn steel: (a) ratcheting strain evolution with number of cycles [34]; (b) ratcheting strain rate evolution [34].

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2.1.3Effects of mean stress direction on uniaxial ratcheting behaviors

Almost all previous research activity has suggested that the direction of ratcheting strain accumulation is identical with the mean stress direction in the absence of pre-straining, complex multiaxial loading or other metallurgical factors. Two tests are conducted on 304 L N stainless steel to find out the effect of mean stress direction on ratcheting performance by Paul et al. [28,36]. Exact same observation has also been reported by Jiang and Sehitoglu [43] for 1070 steel and Wen et al. [44] for Zircaloy-4 (Zr-4) tubes. Fig. 8 demonstrates the ratcheting strain progression curves for two asymmetric stress cycling conditions (engineering stress amplitude of 420 MPa, and engineering mean stresses of +60 MPa and –60 PMa). Absolute values of the ratcheting strains are presented in Fig. 8 for the comparison purpose. In the presence of tensile mean stress uniaxial ratcheting strain accumulation is more than the compressive mean stress. The explanation for this fact is that the experiments are performed under engineering stress controlling mode. Progressively ratcheting strain accumulates in the mean stress direction with stress cycling. Therefore for ratcheting test with tensile mean stress, the true stress increases as the cross-section area of specimen get reduced due to the accumulation of tensile ratcheting strain. However, for ratcheting test with compressive mean stress, the true stress reduces as the cross-section area of specimen increases due to the accumulation of compressive ratcheting strain. As a consequence, true stress levels are different during ratcheting with tensile and compressive mean stresses, higher true stress for tensile mean stress and lower true stress for compressive mean stress. As a result, the rate of ratcheting strain accumulation of the specimen under tensile mean stress is higher than that of compressive mean stress.

Fig. 8.

Uniaxial ratcheting strain evolution with number of cycles at the constant stress amplitude of 420 MPa and stress rate of 50 MPa/s for 304 L N stainless steel: ratcheting strain directions are not considered [28].

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2.2Reversible behavior of ratcheting strain evolution

Paul et al. [45] have conducted a true stress control experiment with constant stress amplitude of 420 MPa and mean stress variation after execution of each cycles between the two values of +60 and –60 MPa. The saturated (i.e., half life) stress-strain hysteresis loop is illustrated in Fig. 9, which depicts a close stress-strain hysteresis loop and an insignificant accumulation of ratcheting strain. This is possible by continuous progression of ratcheting strain in one direction (e.g., tensile) followed by recovery in other direction (e.g., compression). The above experimental observation dictates that the ratcheting strain evolution is reversible in nature. This conclusion does not mean that the ratcheting damage is reversible in nature. Jiang and Sehitoglu [43] have reported similar observation for 1070 steel under step loading condition.

Fig. 9.

Step loading: constant stress amplitude of 420 MPa and mean stress changes alternatively between the value of 60 and –60 MPa: stress vs. strain [45].

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2.3Effect on stress rate

Consequence of stress rate on room temperature uniaxial ratcheting behavior of various metals are investigated by different research groups, like Yoshida [46] for SUS304 stainless steel, Chen et al. [47] for 63Sn/37Pb, Kang et al. [48] for SS304 stainless steel, Lin et al. [39] for AZ91D magnesium alloy and Wen et al. [44] for Zircaloy-4 tubes are few examples. Wen et al. [44] have conducted an extensive study on the effect of stress rate on ratcheting performance of Zircaloy-4 tubes. It is also clear from the ratcheting strain evolution curve in Fig. 10 that the ratcheting strain accumulation is lower for higher applied stress rate, and vise versa. They have also point out that Zr-4 exhibits viscoplastic characteristic.

Fig. 10.

Ratcheting strain evolution with constant mean stress of 180 MPa and stress amplitude of 230 MPa, but different stress rates of 20 MPa/s and 200 MPa/s [44].

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2.4Effect of planar anisotropy

Several auto-grade steel sheets, for example: interfacial free steel (IF), high strength interfacial free steel (IFHS), deep drawing quality steel (DD), extra deep drawing quality steel (EDDQ) and bake hardenable steel (BH) show strong planar anisotropic behavior. Planar anisotropy indicates different material properties (for example yield stress, ultimate tensile stress, uniform elongation, coefficient of normal anisotropy, endurance limit etc.) in different angles with respect to the rolling direction for rolled sheet materials. Paul [50] has shown that IFHS steel exhibits strong planar anisotropic behavior. He has reported that the ratcheting life is the highest in the rolling direction (RD) and lowest in 45° to RD. The deviation of ratcheting life with the angle of specimen’s axis to RD can be clarified from planar tensile anisotropy. IFHS steel displays prominent planar anisotropy in tensile experimentation [49]. The ratio between ultimate tensile strength and yield strength (UTS to YS ratio) is calculated from uniaxial tensile experiment. Paul [49] has calculated that ratcheting life is higher for high UTS to YS ratio. The ratio of UTS to YS is extensively adopted to assess materials capacity to resist local necking [50,51]. Paul [49] also has reported that UTS to YS ratio and ratcheting life vary in a similar way with the orientation of the specimen axis. Ghosh and Gurao [52] have also reported the effect of anisotropy in ratcheting response of pure Ti and 316 stainless steel sheets. They have reported that restricted slip and rapid planar to wavy slip transition lead to buildup of high back stress in 45° sample and hence may cause poor ratcheting life for 316 stainless steel sheet [53].

2.5Effect on loading history

Loading state (i.e., stress amplitude and mean stress) is anticipated to vary with time in real engineering application. Therefore it is extremely important to examine the load history dependency of ratcheting response. Load history dependency of ratcheting can be experimentally measured from ratcheting-ratcheting interaction i.e. step loading (high–low or low–high loading sequence), tensile-ratcheting and ratcheting fatigue interactions. Zhang and Jiang [54] have observed that prior loading history has significant influence on initial cycles but no influence on saturated response for textured OFHC polycrystalline Cu during LCF. Path dependency of any plastic deformation is well known and ratcheting is one of the cyclic plastic deformation phenomena. This implies that the ratcheting response extensively depends upon loading history. Path dependency of ratcheting can be explained from dislocation movement and interaction with obstacles. Normally plastic deformation is the outcome of dislocation movement, number of dislocations and the change in their arrangement with progression of plastic deformation. As tensile pre-stressing alters the number of dislocations and their arrangement, ratcheting response varies with tensile pre-stressing. Paul et al. [36] have investigated the effect of tensile pre-stressing on uniaxial ratcheting response on SA333 CMn steel under true stress controlled test. They have reported that symmetric stress cycling (i.e., zero mean stress) without pre-stressing results in negligible accumulation of ratcheting strain. However, compressive ratcheting strain accumulation is noticed for tensile pre-stressing. And ratcheting strain accumulation rate increases with degree tensile pre-stressing. Usually, the direction of mean stress and accumulation of ratcheting strain are alike i.e. tensile (compressive, respectively) mean stress results in tensile (compressive, respectively) ratcheting strain [36]. Even for ratcheting experiment with tensile mean stress, tensile pre-stressing leads to ratcheting strain build up in the compressive direction for initial few cycles and afterward tensile ratcheting strain builds up in the succeeding cycles. Wang et al. [55] have observed that tensile pre-strain improves ratcheting (asymmetric stress cycling with tensile mean stress) life, while compressive pre-strain deteriorates the ratcheting life.

Experiments with step loading are normally conducted to understand the dependency of material’s load history on ratcheting. In high-low loading sequence (i.e., high to low step loading), the specimen is loaded to a constant high mean stress or amplitude stress till saturation, and afterwards lower constant mean stress or stress amplitude loading. Paul et al. [45] have investigated the effect of step loading on uniaxial ratcheting response on 304 L N stainless steel under true stress controlled test. In step loading test, the mean stress or stress amplitude alters after continuous cycling of 0.25 life fraction, after which the next step starts. Paul et al. [45] have assumed that the material’s stress-strain response becomes stabilized after cycling 25% of number of cycles to failure. In the low to high stress amplitude step loading test, the stress amplitude changes in ascending order of 300, 360 and 420 MPa in three steps, whereas mean stress remains constant at 120 MPa. For each step, a significant amount of ratcheting strain accumulation is noticed and the ratcheting strain accumulation rate reduces with number of cycles. Similarly, in the low to high mean stress step loading test, the mean stress varies in increasing order of 60, 120 and 180 MPa in three steps, whereas constant stress amplitude of 420 MPa is maintained during all the three steps. For each of the steps of low to high mean stress step loading, ratcheting strain build-up rate declines with the number of cycles. On the other hand, in high to low mean stress step loading test, fixed stress amplitude of 420 MPa is maintained during all the three steps, while the mean stress alters in decreasing order of 180, 120 and 60 MPa in three steps. The considerable amount of ratcheting strain accumulation is noticed during the first step only (stress amplitude of 420 MPa and mean stress of 180 MPa). Complete ceasing of ratcheting strain progression i.e. plastic shakedown is observed from the second steps onwards (i.e., cycling with mean stress of 120 and 60 MPa). The ratcheting life increases drastically (almost doubles) in high to low mean stress step loading in comparison with low to high mean stress step loading. Similarly, in high to low stress amplitude step loading test, the stress amplitude alters in declining order in three steps of 420, 360 and 300 MPa, whereas mean stress of 120 MPa maintained constant in all three steps. Only in the first step (stress amplitude of 420 MPa and mean stress of 120 MPa), a substantial amount of ratcheting strain evolution is noticed. From the second steps onwards, the plastic shakedown occurs, i.e. ratcheting strain accumulation ceases. In comparison with low to high stress amplitude step loading, the ratcheting life increases considerably (almost doubles) in high to low stress amplitude step loading test. Paul et al. [45] have explained the increase of ratcheting life in high to low (stress amplitude or mean stress) step loading in comparison with low to high step loading by ratcheting damage mechanism. In ratcheting, simultaneously two damaging mechanisms (Fig. 4) become active: (i) fatigue damage and (ii) directional strain accumulation. During high to low step loading, from the second step onwards the directional strain accumulation does not take place and only fatigue damage becomes active. Between the two damage mechanisms, only one is active during high to low step loading; as a result ratcheting life increases. The same observation is also reported in Zircaloy-4 tubes [44], U71Mn rail steel [56], SS304 [57], 316 L stainless steel by Kang et al. [58], high-nitrogen steel X13CrMnMoN18-14-3 [59] and zirconium alloy tubes [60].

2.6Effect of loading path

The experimental ratcheting behavior studied in the literature corresponds to a special case of a large variety of complex and loading history dependent ratcheting response, which is feasible in practice. Moreover, the ratcheting performance under prolonged cyclic loading is the most concern for structural integrity. Many studies have investigated the influence of loading path (i.e., proportional and non-proportional loading) on ratcheting strain accumulation rate. Majority of researchers investigate the ratcheting behavior under proportional and non-proportional axial-torsion loading conditions using a tubular specimen. Bocher et al. [61] have studied the ratcheting response under three dimensional (i.e., 3D) stress state including hoop, axial, shearing and radial components. In or out of phase strain controlled cycles are applied in the two directions, while in the other direction stress remains constant. They have revealed that the accumulation of ratcheting strain increases with phase lag between the cyclic components. The effect of loading path on multiaxial ratcheting is discussed in detail as follows.

Normally, we define the ratcheting as asymmetric stress cycling. But for biaxial or multi-axial case, the presence of mean stress in any axis and stress (or strain) cycling leads to the development of ratcheting strain along the mean stress direction. Biaxial strain controlled ratcheting response has traditionally been investigated by two types of tests. In the first type of test, a constant axial load is applied in a thin walled circular tube and on top of it, symmetric strain controlled torsional cycling is also applied. The constant axial stress acts as mean stress and its interaction with cyclic shear stress results in buildup of axial ratcheting strain (i.e., continuous elongation of the tube). Wood and Bendler [22] have reported various micromechanical findings on the slip systems related phenomenon during symmetric strain controlled torsional cycling of thin walled circular Cu tubes with a constant axial load. There are many earlier reports also available for similar types of experimentation conducted by Moyar and Sinclair [21], Benham [24], Freudenthal and Ronay [62], Portier et al. [63], Gao et al. [64] and Chen et al. [65].

The second type of test involves symmetric axial/shear strain cycling of a thin walled tube at steady internal pressure. The interaction between the axial/shear and circumferential stresses leads to a continuous rise in the diameter of the tube (circumferential ratcheting strain). Progressive collapse of pressure vessels can be observed under this type of loading. Ruiz on 1967 [66] has investigated the progressive collapse of pressure vessels under symmetric strain controlled axial cycling with constant internal pressure (i.e., circumferential stress). This type of test has been extensively adopted in both LCF studies and in cyclic plasticity modeling investigations. Hassan and Kyriakides [67] have investigated strain controlled ratcheting experiments with internal pressure in tubular specimen of SS304 stainless steel. The accumulation rate of circumferential ratcheting strain rises with increase in internal pressure.

Similar to the strain cycling, biaxial ratcheting with stress cycling is also possible in four ways: (i) symmetric stress controlled torsional cycling with constant axial stress, (ii) symmetric axial stress controlled cycling with constant shear mean stress, (iii) symmetric stress controlled torsional cycling with constant internal pressure, and (iv) symmetric axial stress controlled cycling with constant internal pressure. One example of biaxial ratcheting is discussed in Fig. 11. Jiang and Sehitoglu [68] have conducted stress controlled non-proportional ratcheting test on 1070 steel. They have kept the constant axial mean stress of 300 MPa and variable shear stress with the amplitude of 230 MPa within a cycle. Fig. 11(a) shows axial-torsion loading path, consisting of symmetric cyclic shear and fixed axial stress. This loading path is non-proportional in nature as the ratio of axial stress to shear stress varies during a cycle. The axial-shear strain evolution is depicted in Fig. 11(b). The axial strain accumulates in the axial mean stress direction (i.e., tensile direction), whereas there is no accumulation of strain in the shear direction. Like uniaxial experiments, the ratcheting strain accumulation rate reduces with number of cycles in this experiment as well.

Fig. 11.

Experimental ratcheting for a non-proportional tension-torsion loading path consisting of constant axial stress and alternating shear. (a) stress-controlled loading path [68]; (b) biaxial strain response [68].

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Usually, biaxial and multi-axial ratcheting tests are conducted in tubular specimen [67–69]. In tubular specimen, loading is possible in three axis, viz. axial, shear or torsion, hoop or internal pressure. If mean stress is introduced in any one axis and cyclic stress or strain is introduced in the remaining two axes or in all three axes, then ratcheting is also possible.

It is well established that the driving force of ratcheting strain progression is the mean stress, whereas the ratcheting strain accumulation rate depends upon stress amplitude, mean stress and loading history. Aubin et al. [69] have conducted ratcheting experiments with four loading paths (i.e., shear, axial, square and cross) that have the identical mean stress and comparable equivalent stress amplitudes. Aubin et al. [69] have concluded that the degree of non-proportionality due to difference in loading paths is responsible for different ratcheting rate. Similarly, Kang et al. [70] have also demonstrated the influence of non-proportional loading on ratcheting strain evolution.

2.7Effect of temperature on ratcheting

Temperature has a prominent effect on ratcheting strain evolution and ratcheting life. Yu and Kumar [71] have conducted ratcheting experiment with stress ratio (R) of 0.1 and stress range of 80% of the UTS on annealed Mo. Variation of YS and UTS with temperature is depicted in Fig. 12(a) for annealed Mo. The annealed Mo displays softening behaviour with increasing temperature. To neutralize the temperature softening effect, Yu and Kumar [71] have conducted ratcheting experiment with stress range of 80% of the UTS at that particular temperature. The YS and UTS fall quickly with rising temperature in the tested temperature range. Yu and Kumar [71] have reported that as the difference between YS and UTS is retained with rising temperature, there is no considerable loss in work hardening at that temperature. The ratcheting strain evolution with number of cycles is depicted in Fig. 12(b) for stress range of 80% of the UTS at various temperatures. They have examined the ratcheting response in 100 °C temperature gaps from 100 °C to 500 °C. Fig. 12(b) illustrates that the number of cycles to failure decreases and accumulation of ratcheting strain increases with rising temperature. Yu and Kumar [71] have explained the boost in ratcheting strain accumulation with rising temperature by dislocation activity through transmission electron microscopy (TEM) images. At ambient temperature, dislocations generated by cyclic loading are progressively arranged themselves into cell structures with increasing cycles. At elevated temperature, well-defined cell structures are formed in less number of cycles than at ambient temperature. After sufficient number of cycles, the cells begin to transform into sub-grains to lessen the overall strain energy. Portier et al. [63] have also revealed that during multiaxial ratcheting on 316 austenitic stainless, the accumulation of ratcheting strain enhances with increasing temperature. Liu et al. [72] have conducted ratcheting test at 650 °C on GH4169 superalloy and reported that apart from high temperature oxidation, the interaction between grain boundary and slip band are the prime factors for intergranular damage. They have also reported that transgranular fracture mode is visible below 600 MPa stress amplitude symmetric stress cycling, while the mixed intergranular and transgranular mode is noticed above 600 MPa stress amplitude symmetric stress cycling, and the mixed intergranular and transgranular mode is always visible for asymmetric stress cycling. Yu et al. [73] have reported a tendency to shakedown in zero-to-tension stress cycling at high temperatures on Z2CND18.12 N stainless steel due to dynamic strain aging (DSA) effect. Similarly, Yuan et al. [74] have also noticed shakedown of 316 L N austenitic stainless steel in cyclic bending loading due to DSA. Liang et al. [75] have noticed that ratcheting strain accumulation increases and ratcheting life reduces with rising thermal aging temperature and increasing thermal aging time.

Fig. 12.

(a) Monotonic tensile properties for annealed Mo in the temperature range from room temperature to 500 °C: the variation in yield strength and ultimate tensile strength with test temperature is shown [71], and (b) effect of temperature on the cyclic response (ratcheting strain evolution with cycles) of annealed molybdenum for applied stress range of 80% of the UTS [71].

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3True stress controlled experiment

The ratcheting behaviour has been investigated by the majority of researchers by controlling load or engineering stress, which is calculated from the initial cross sectional area of the specimen. If accumulated ratcheting strain is small and not capable to noticeable alteration of the specimen dimension, then this consideration could be valid. However, for some specific loading condition like, high magnitude of mean stress and stress amplitude, the high accumulated ratcheting strain can significantly alter the specimen cross-sectional area.

Paul et al. [28,33] have demonstrated that without introduction of an appropriate correction factor for the alteration of cross sectional area, the true stress amplitude and true mean stress increase uncontrollably, and as a result specimen fails by necking rather than fatigue crack initiation and propagation. From the engineering application point of view, as measurement and regulation of true stress/strain cannot be possible in the actual operational field, so engineering stress controlled ratcheting experiment is essential. However from the material point of view, true stress controlled test is indispensable to characterize and model the ratcheting response of materials. Paul et al. [28,33,36] have argued that it is extremely difficult to choose a safe percentage of ratcheting strain accumulation with the intention that cross sectional area alteration in specimen could be ignored. To avoid all complexities in decision making, it is a good practice to investigate the ratcheting response of the material under true stress control mode irrespective to the amount of ratcheting strain accumulation. Paul et al. [28,33,36] have investigated the uniaxial ratcheting behaviour of SA333 CMn steel under both engineering and true stress controlled modes to understand the difference between the two stress controlling modes. The evolution of true stress and true ratcheting strain during an engineering stress control test are illustrated in Fig. 13(a) for SA333 C-Mn steel (loading condition: mean stress of 80 MPa and stress amplitude of 310 MPa). For this test condition, a considerable amount of ratcheting strain is build up.

Fig. 13.

For SA333 C-Mn steel (a) Alteration of true maximum stress and stress amplitude with number of cycles in engineering stress control test [33], (b) true ratcheting strain versus number of cycles plot for stress amplitude of 350 MPa and mean stress of –40, 0, 40, 80 and 120 MPa [33] (c) number of cycles to failure, hysteresis loop area and plastic strain amplitude versus mean stress plot [33], and (d) true stress-strain plot of saturated cycle, compressive tip of hysteresis loops are translated to common origin [33].

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By considering the volume incompressibility condition, true stress can be determined from Eq. (2).

where, σ and εr are true stress and true ratcheting strain, S and er are engineering stress and engineering ratcheting strain.

Volume incompressibility condition is applied to calculate the area reduction.

where, ΔA is the reduction in cross sectional area at er ratcheting strain and A is the initial cross sectional area.

Paul et al. [28,33] have reported that around 50.5% engineering ratcheting strain is accumulated before failure of the SA333 C-Mn steel specimen. Buildup of such huge ratcheting strain can result in 1.505 time rise in the actual true stress level, and as well 33.56% lessening in cross-sectional area of the specimen. This considerable decline in cross-sectional area can create an uncontrollable rise both in the true stress amplitude and maximum stress, while the corresponding engineering stresses are continued at constant levels.

Around 50.5% elongation in tensile direction for SA333 steel is attained during engineering stress controlled uniaxial ratcheting experiment while tensile uniform elongation is approximately 17.18%. Therefore, Paul et al. [45] have concluded that accumulated ratcheting strain before necking is much higher than the tensile uniform elongation of the material. Paul et al. [45] have shown that the maximum true stress during tensile necking (at the point of maximum load) and in uniaxial ratcheting instability are analogous. As a fixed maximum engineering stress is maintained during engineering stress controlled ratcheting experiment, more accumulation of engineering ratcheting strain compare to engineering tensile uniform elongation is required to achieve constant true ultimate tensile stress. However, more research effort is needed to reveal completely this fact.

The progression of ratcheting strain in true stress controlled experiment in SA333 C-Mn steel is illustrated in Fig. 13(b). Similar to engineering stress controlled experiment, ratcheting strain buildup along the mean stress direction and ratcheting strain accumulation rate decay with number of cycles are also noticed for true stress controlled test. For true stress controlled ratcheting test, initially higher ratcheting strain accumulation rate is noticed followed by a steady decline and then become stable at a constant rate for its remaining life. The tertiary zone is shortened in true stress controlled ratcheting test. With increase in mean stress, both the ratcheting fatigue life and accumulated ratcheting strain increase. Paul et al. [33] have explained the improvement in ratcheting life by reduction of plastic strain energy with increasing mean stress. The enclosed area of stress-strain hysteresis loop is normally represented by plastic strain energy density. Increasing the plastic strain energy, the fatigue life becomes shorter as the material absorbs more energy in each cycle [68]. The plastic strain energy computed from stable stress-strain hysteresis loop is plotted with mean stress in Fig. 13(c). Evolution of plastic strain amplitudes is also included in the same figure. If the zero mean stress condition is considered as a reference, the plastic strain energy declines with increasing mean stress (Fig. 13(c)) and this phenomenon is known as mean stress dependent hardening [28,33]. Simultaneously, it is also noticed that the plastic strain amplitude declines with growing mean stress. The result confirms that the reduction of both plastic strain amplitude and plastic strain energy with increasing mean stress lead to improvement of ratcheting life. A similar mean stress dependent hardening behavior has been reported in carbon steel [76,77], 304 stainless steel [78–80], polycrystalline Cu [81,82] and polycrystalline Ni [83]. The mean stress dependent hardening is explained by Paul et al. [28,33] by experimentation on SA333 C-Mn steel. The saturated cycle stress-strain responses are shown in Fig. 13(d). All the stress-strain hysteresis loops in Fig. 13(d) are translated to a common origin (0, 0) for the purpose of comparison. The hysteresis loop size reduces and the non-linear portion of the loading branch becomes steeper with rising mean stress. Paul et al. [28,33] have reported that the mean stress dependent alteration of stress-strain hysteresis loop is observed right from the first cycle.

3.1Comparison between true and engineering stress controlled tests

Comparison between engineering and true stress controlled testing modes provides an idea regarding the importance of cross sectional area correction in ratcheting experiments, specially where the accumulation of ratcheting strain is high. In true stress controlled ratcheting experiment, continuously cross sectional area of the specimen and accordingly the applied load levels are corrected from the feedback of ratcheting strain. Whereas, engineering stress controlled ratcheting experiments are conducted by controlling maximum and minimum peak load, the accumulated ratcheting strain has no influence in load calculation. Paul et al. [28,33] have conducted engineering and true stress controlled ratcheting tests separately while maintaining all other experimental conditions alike to represent the difference between the true and engineering stress controlled ratcheting tests. Evolution of ratcheting strain with number of cycles is compared in two test controlling modes for SA333 C-Mn steel in Fig. 14. The fatigue life is improved in true stress controlled test, while the accumulation of ratcheting strain is less in true stress controlled experiment. The reason for the reduction in ratcheting fatigue life during engineering stress controlled test with tensile mean stress is thought to be due to (i) fast buildup of ratcheting strain than in true stress controlled test, (ii) a constant rise in the true stress as observed in Fig. 13(a), (iii) instability and necking are formed because of massive decrease in cross-sectional area. In contrast, failure always takes place by initiation and propagation of fatigue cracks during true stress controlled ratcheting tests. Fig. 14 depicts that both the engineering and true stress controlled experiment modes generate almost equal amount of ratcheting strain buildup in initial few cycles. As the cycling progresses, the ratcheting strain accumulation in two experiment controlling modes is mostly diverse. Paul et al. [33] have suggested the true stress controlled tests to characterize the ratcheting response of materials, exclusively for large ratcheting strain accumulation. But, it is extremely tricky to indicate a cycle/strain limit under which an engineering stress controlled experiment would provide satisfactory result. Therefore, Paul et al. [28,33] have suggested that true stress controlled ratcheting experiment, irrespective of buildup, would be a good practice.

Fig. 14.

Comparison between true and engineering stress control ratcheting test: mean stress of 80 MPa and stress amplitude of 310 and 350 MPa for SA333 C-Mn steel [33].

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4Remaining life assessment

Progression of damage by means of nucleation and growth of defects, such as micro-voids during tensile deformation and micro-cracks during fatigue, and their coalescence into macro-cracks, eventually results failure of metals in different loading conditions [84,85]. Kachanov [86] has first introduced the term ‘damage’ to predict the in-service creep failure of metals at high temperatures [86]. Continuum damage mechanics (CDM) is developed to measure average material degradation at a macro-mechanics scale, while material degradation in a micro-mechanics scale is cover by damage mechanics. In the CDM hypothesis, it is assumed that once the specified value of damage variable arrives at definite level, the failure occurs as the material unable to sustain the applied load.

In brief, damage measurement technique can be classified into four categories (Fig. 15). Change in mechanical behavior is the most reliable and direct measurement technique, and which can be easily incorporated in to finite element based damage model. Damage in materials may be reflected by some physical properties of materials like density, electrical resistance and ultrasonic velocity. Microstructure based damage measurement techniques are also a direct measurement technique, but cumbersome for true damage representation and quite difficult to incorporate in finite element based damage model.

Fig. 15.

Various damage measurement techniques.

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Paul et al. [37] have conducted tensile test on interrupted pre-ratcheting 304 L N stainless steel specimens. Pre-ratcheting test with stress amplitude of 420 MPa and mean stress of 120 MPa is interrupted at 50, 450 and 1500 cycles i.e. ratcheting life fractions (Drt) of 0.025, 0.23 and 0.76. The Drt can be defined as the ratio of Nr and Nfr for the same test condition, where Nr is the number of cycles in the interrupted experiment and Nfr is the number of cycles to failure in uninterrupted ratcheting experiment. Fig. 16(a) shows the tensile stress-strain responses after various levels of ratcheting damage i.e. at different Drt. The alteration in tensile performance i.e. yield stress (YS), ultimate tensile stress (UTS) and uniform elongation with Drt (i.e., various levels of ratcheting damage) are shown in Fig. 16(b). YS and UTS increase, and uniform elongation (εul) decreases with increasing Drt. Initially, the increment of YS and UTS are large, and with number of cycles the increment rate decreases and maintained a stable value, while εul decreases initially in a faster rate and then get saturated. Dutta and Ray [41] have also reported similar degradation of tensile performance with ratcheting damage for interstitial free (IF) steel.

Fig. 16.

Ratcheting with mean stress 120 MPa and stress amplitude 420 MPa interrupted at 50, 450 and 1500 cycles i.e. at 0.1, 0.25 and 0.75 of ratcheting life fractions (DN) followed tensile test (a) tensile stress-strain curve [37] (b) Yield stress, ultimate tensile stress and uniform elongation variation with ratcheting life fractions (DN) [37].

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4.1Ratcheting-fatigue interaction

The material deforms in the plastic domain and prominent stress-strain hysteresis loop is formed during both LCF and ratcheting. The basic difference between LCF and ratcheting is the directional strain accumulation. Prominent directional progressive strain accumulation is noticed for ratcheting, while no directional strain accumulation is noticed for LCF. In this section, the effect of ratcheting strain buildup on consequent LCF behavior is discussed. Paul et al. [37] have reported ratcheting-LCF interaction in 304 L N stainless steel. They have selected ratcheting experiment with stress amplitude of 420 MPa and mean stress of 60 MPa, and LCF experiment with strain amplitude of 0.7%. The reason behind the selection of those loading conditions can be stated as: the average stress amplitudes in LCF and ratcheting are comparable. As a result, the path dependent effect in plasticity (i.e., strain range effect, cyclic hardening/softening depending on loading sequence etc.) can be avoided.

Paul et al [37] have reported that the ratcheting life is approximately 1980 cycles during ratcheting test with mean stress of 60 MPa and stress amplitude of 420 MPa. They have interrupted the ratcheting experiments at 198, 450 and 990 cycles i.e. 0.1%, 0.25% and 0.5% of its ratcheting life. After pre-ratcheting, LCF experiments are carried out with strain amplitude of 0.7%. LCF responses (i.e., stress amplitude versus number of cycle) with different pre-ratcheting histories are illustrated in Fig. 17(a). The material also shows cyclic hardening response in all pre-ratcheting conditions i.e. stress amplitudes are located far on top of the pure LCF response. Material shows major initial cyclic hardening followed by gradual cyclic softening for pure LCF, while early mild cyclic hardening followed by mild cyclic softening is noticed for pre-ratcheting conditions. LCF life fraction (Dlcf) is the ratio of Nlcf and Nflcf, where Nlcf is the LCF life in pre-ratcheting samples and Nflcf is the fatigue life in pure LCF. Fig. 17(b) illustrates the Dlcf versus Drt. If, Dlcf versus Drt plot follows Miners damage law (summation of their damage fraction is equal to one) [37] i.e. a linear curve with 135° inclined to horizontal axis, then it can be stated that pre-ratcheting have no considerable influence on its successive LCF life. Paul et al. [37] have concluded that pre-ratcheting has a considerable damaging effect on its successive LCF life as the curve is concave in nature. The directional strain buildup in pre-ratcheting sample is the prime cause for such variation in LCF response.

Fig. 17.

(a) Stress amplitude response in LCF after pre-ratcheting: Ratcheting at mean stress 60 MPa and stress amplitude 420 MPa followed by LCF at 0.7% strain amplitude [37], and (b) Remaining LCF life fraction versus ratcheting damage fraction during pre-ratcheting [37].

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4.2Ratcheting-creep interaction

The time dependent permanent deformation of metals at elevated temperature under static loading is well known as creep phenomena. Some face center cubic (FCC) metals, like austenitic stainless steels, show creep even at room temperature [45]. The LCF-creep interaction is well known to the research community. Kang et al. [48] have demonstrated the role of the peak strain hold on cyclic hardening under LCF for SS304 stainless steel at ambient and elevated temperatures. In the same way, Yoshida [46] has carried out various uniaxial and biaxial creep-ratcheting interaction experiments at ambient temperature. He has reported the result of peak stress hold and stress ratio on ratcheting. Similarly increase in ratcheting strain accumulation with peak stress holding time is also reported by Chen et al. [60] for zirconium alloy. The experimental results of Kang et al. [48] on SS304 stainless steel at ambient and elevated temperatures are utilized to discuss the ratcheting-creep interaction in this section.

Kang et al. [48] have carried out uniaxial ratcheting on SS304 stainless steel at 700 °C temperatures without peak stress hold, and with peak stress hold for 5 seconds and 10 seconds. Fig. 18 shows that the peak stress hold time even at 700 °C temperature influences the ratcheting strain accumulation. As the absolute value of tensile peak stress is higher than compressive valley stress during the asymmetrical stress cycling with tensile mean stress, the creep strain accumulation in tensile peak stress hold is partly recovered during compressive valley stress hold, and finally a resultant tensile creep strain is build up for a particular cycle. As a consequence, the larger ratcheting strain accumulation during the peak/valley stress hold with prolong hold-time is the result of larger creep strain evolution. In fact, two types of strain accumulation take place during asymmetric stress cycling with the peak/valley stress hold (i) time-independent plastic strain accumulation i.e. ratcheting strain (ii) time-dependent plastic strain accumulation i.e. creep strain which is due to the visco-plasticity of the material. The ratcheting strain accumulation at 700 °C with peak stress hold time is depicted in Fig. 18. Kang et al. [48] have reported that the time-dependency of ratcheting at 700 °C is also greater than that at room temperature even for multiaxial cyclic stressing. They have also concluded that the effect of hold-time on the multiaxial ratcheting is normally less than that uniaxial ratcheting.

Fig. 18.

Results of axial ratcheting (40 ± 100 MPa) with or without peak/valley stress hold, at 700 °C and stressing rate of 10 MPa/s for SS304 stainless steel: curves of ratcheting strain vs. cyclic number with different hold-times [48].

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5Ratcheting in component level

Ratcheting behavior is essential in the design of many mechanical parts (like pipes of power plants, railways and turbine rotors) which are exposed in thermo-mechanical cyclic loading. The piping fittings used in chemical industries and nuclear power plants play a critical function in secured operation. An internal fluid pressure acts as mean load/stress in the pipelines and on top of it cyclic loading can be produced by variation of fluid pressure or alteration of temperature or other sources like seismic loading. To understand the ratcheting phenomenon proficiently, full scale (i.e., component level) experimentation is mandatory along with specimen level experimentation.

Several investigators have illustrated the experimental ratcheting response under reverse bending in pressurized elbows and straight pipes. Local wall thinning of pipes caused by mechanical damage and crack repair, erosion of outside soil and rainwater can intensify the ratcheting effect. The local stress distribution is a little bit complex in the elbow because of its geometry. Therefore, extensive research has conducted by various research groups to know the ratcheting performance of straight pipe with local thinning in order to sustain the piping system integrity. Yoshida et al. [87] have investigated biaxial ratcheting response in a carbon steel pipe under constant internal pressure and simultaneous cyclic load. Kulkarni et al. [88] have conducted ratcheting experiment on SA 333 Gr. 6 carbon steel pipe with steady internal pressure and repeated bending load. They have reported that evolution of ratcheting strain takes place in the circumferential direction, while no build-up of ratcheting strain occurs in longitudinal direction of a pipe. Yahiaoui et al. [89] have conducted ratcheting experiment on long and short radius elbows made of carbon and stainless steels under steady internal pressure and cyclic in-plane bending. They have reported that ratcheting strain accumulation is higher in the crown hoop direction than in the axial direction. Yahiaoui et al. [90] have also conducted ratcheting test on elbows under constant internal pressure and out-of-plane cyclic bending. They have reported that the maximum ratcheting strain accumulation occurs in the hoop direction and not in the direction of maximum principal strain. Chen et al. [91] have investigated the ratcheting behaviour of low carbon steel pipe under reversed bending and internal pressure. They have noticed that the ratcheting strain accumulates in the hoop direction and the ratcheting strain accumulation rate increases with rising loading level. However, ratcheting strain accumulation rate reduces or even vanishes during high to low step cyclic bending load. Chen et al. [92] have also reported that the ratcheting strain evolution rate grows with an enhancement of internal pressure at constant cyclic bending load or a rise of the cyclic bending load at steady internal pressure.

Vishnuvardhan et al. [93] have conducted ratcheting studies on four elbows and four straight pipes exposed to constant internal pressure and cyclic bending load. They have conducted all the tests in displacement control by applying different levels of load-line displacement in the specimens. They have selected the elbow with the total length of 1342 mm, being 225 mm radius of the bent portion and 500 mm length of straight portions. The average initial thickness of the elbows lies within 14.7 to 15.1 mm. To include the boundary effects in the elbow, the straight portions are supplied. Vishnuvardhan et al. [93] have reported that the elbows fail by formation of axial through-wall crack and followed by simultaneous swelling (ballooning) and thinning. In all the four failed elbow specimens, cracks are detected in the crown of bent portion. The through wall crack is detected by a spiky water jet, as shown in Fig. 19(a). Fatigue life depends upon the amplitude of cyclic displacement and amount of internal pressure. The decline in thickness is calculated at around 12–15%. Fig. 19(b) illustrates the percentage rise in diameter versus the number of cycles for the elbow. The bend clip is fitted in elbow to measure the change in diameter. Shi et al. [94] have studied the ratcheting behaviour of pressurized Z2CND18.12 N stainless steel (YS = 388 MPa and UTS = 590 MPa) elbows under fixed internal pressure of 17.5 MPa and in-plane cyclic bending with an axial cyclic load of 20 kN. The ratcheting strain is accumulated mainly in hoop direction at the extrados, crown, 45° position and intrados. The hoop ratcheting strain has the maximum values at intrados follows by crown. During the early cycles, the accumulation rate of hoop ratcheting strain declines with growing number of cycle, and then maintains a steady rate.

Fig. 19.

(a) Occurrence of through-wall crack indicated by a sharp water jet: ratcheting experiment conducted with internal pressure of 39.2 MPa and displacement of ±41 mm i.e. maximum load range ±272 kN [93], (b) Percentage increase in diameter vs. number of cycles during ratcheting test on the elbow specimen with internal pressure of 37.9 MPa and displacement of ±51 mm i.e. maximum load range ±309 kN [93].

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Vishnuvardhan et al. [93] have selected the straight pipes length of 2800 mm with the average initial thickness of 14.3–15.3 mm. The thickness is reduced to 12.0 mm by machining in the centre of the pipe with a gauge length of 200 mm. They have observed that the straight pipe fails either by the formation of through-wall crack, along with ratcheting ballooning and thinning or bursting with simultaneous thinning and ballooning. They have measured the thickness of the pipe before and after the test at all the grid points printed before the experiment. In the gauge portion of the straight pipe, 13.4–19.0% ballooning is noticed. From the comparative study, Vishnuvardhan et al. [93] have drawn the conclusion that the ratcheting is more severe in straight pipe than in elbow.

6Progress in microstructural observation

Initially ratcheting research has started on the macroscopic experimentation and constitutive modelling to simulate ratcheting behaviour. Conversely, the majority of the constitutive models are phenomenological in nature and build up entirely based on the macroscopic experimental observation only. As a consequence, constitutive models with many material parameters have been developed and these models are not user-friendly. Therefore its use is limited in engineering application. The advanced phenomenological models application is limited because of oversensitivity of material parameters and limitation of use in verity of materials and loading conditions. For that reason, two and half decades old tri-segmented Chaboche [95] or nonlinear Zigler [96] models are still used in engineering modelling work. The previous review done by Ohno [97,98], Chen et al. [99], Kang [100] and Chen et al. [101] have mainly emphasized on constitutive models. Most of the developed models are unable to provide a precise simulation of the ratcheting strain accumulation for the materials with different cyclic hardening/softening features, different loading histories, and complex multiaxial loading paths. Therefore, it is extremely important and essential to understand the microstructural evolution (i.e., micro-mechanism) in ratcheting. Recently, some microstructural investigation has been conducted by Gaudin and Feaugas [30], Feaugas and Gaudin [31], Kang et al. [102–104], Dong et al. [105,106], Dutta et al. [42], Sarkar et al. [107], Yu and Kumar [71] and Lin et al. [38] on metals.

Kang et al. [103] have investigated the uniaxial ratcheting behaviour of ordinary 20 carbon steel (0.19% C, 0.22% Si, 0.46% Mn) (polycrystalline body-centered cubic (BCC) metal) by macroscopic and microscopic observations at ambient temperature. They have noticed the development of dislocation patterns from some low density modes (i.e., dislocation lines and networks) to high density modes (i.e., dislocation tangles, walls and cells) with number of cycles during LCF and ratcheting. The sub-grains are created by the re-arrangement of dislocations after a certain number of cycles in ratcheting.

Kang et al. [104] and Dong et al. [105] have examined the microstructural evolution during uniaxial and multiaxial ratcheting of 316 L stainless steel. The 316 L stainless steel has face centered cubic (FCC) crystal structure and also has low stacking fault energy (SFE, 15 mJ/m2[33]). For 316 L stainless steel, the progression of dislocation patterns is also similar as observed in 20 carbon steel during uniaxial and multiaxial ratcheting (i.e., dislocation arrangement alters progressively from the low density patterns to high density patterns). However due to the low stacking fault energy of 316 L stainless steel, the cross slip is not activated and dislocation cell is the stable dislocation arrangement for both the case of uniaxial and multiaxial ratcheting. On the other hand, for BCC 20 carbon steel sub-grain is the stable dislocation pattern during the ratcheting since the dislocation cross-slip is readily achievable in the BCC crystals. The comparatively higher ratcheting strain accumulation rates in BCC 20 carbon steel during uniaxial and multiaxial ratcheting at the stage II are normally caused by the dislocation re-arrangement during the development of sub-grain and activation of dislocation slip within the sub-grain.

Kang et al. [102] have investigated the uniaxial ratcheting response of Ti–6Al–4 V alloy with two phases (i.e., primary α phase with hexagonal close packed (HCP), and secondary β phase with BCC crystal structures) at room temperature. They have noticed the progression of dislocation arrangement and formation of deformation/mechanical twin during uniaxial ratcheting. The dislocation density and the number of twins grow with number of cycles. Neither the dislocation wall nor cell is found in their investigation. They have only observed the activity of planar dislocation evolution in association with development of discrete dislocation lines, dislocation nets and parallel lines. Gaudin and Feaugas [31] and Feaugas and Gaudin [30] have studied the micromechanism of ratcheting quantitatively for the for AISI316 L stainless steel. They have observed that no ratcheting strain evolution (i.e., cyclic creep) takes place during the cyclic plastic deformation with planar slip activity. The plastic deformation could be recovered completely during the cyclic plastic deformation with planar slip activity because of the smooth movement of dislocations. Conversely, accumulation of ratcheting strain takes place during cyclic plastic deformation with cross slip activity as the unrecoverability of slip may possible be due to the increased resistance of dislocation movement during the cross slip. Lin et al. [38] have reported that twin density and ratcheting strain increase with increasing mean stress and stress amplitude. Twinning is the only active deformation mode in hot-rolled AZ31B magnesium alloy, as a result straining along the c-axis is only possible at room temperature [38]. Yu and Kumar [71] have conducted uniaxial ratcheting experiments on recrystallized Mo sheet at ambient and high temperatures. They have noticed that at elevated temperature, well-defined cell structures are developed in less number of cycles, and sub-grains are transformed from dislocation cells after a large number of cycles to minimize the overall strain energy. Whereas at room temperature, only cell structures are observed, and no sub-grains are noticed. Sarkar et al. [107] have pointed out that elastic shakedown is manifested as a random arrangement of isolated dislocation tangles, whereas cellular dislocation patterns are developed during rapid strain accumulation as a result of continuous ratcheting. Dutta et al. [42] have detected that the dislocation density of ratcheted samples enhances with rising mean stress at fixed stress amplitude in 304 L N stainless steel. They have also observed from X-ray diffraction examination that deformation induced martensite (DIM) is generated during ratcheting on 304 L N stainless steel, and the volume fraction of DIM increases with growing ratcheting strain. In addition, additional dislocations can be generated at the time of martensitic transformation during ratcheting [42].

Paul et al. [100] have used EBSD data of DP 780 steel to quantitatively measure differences between LCF and ratcheting test samples. The average misorientation maps for the LCF and ratcheting specimens are depicted in Fig. 20. Paul et al. [108] have reported that there is a significant difference in the local in-grain misorientations for LCF and ratcheting. The local in-grain misorientation is higher in ratcheting in comparison with LCF specimen. This is consistent with the observation of dislocation sub-structure by other researchers. The ferrite misorientation is larger compared to the average around the martensite islands. This is direct confirmation of strain localization at the ferrite/martensite interface in the ferrite.

Fig. 20.

EBSD orientation maps for two different test conditions, LCF (total strain amplitude of 0.5%), and Ratcheting (mean stress of 150 MPa and stress amplitude of 550 MPa). All Euler orientation maps are shown on the left with grain boundaries >10° shown in bold black lines, and grain boundaries between 3° and 10° shown in fine black lines. Local misorientation maps shown to same scale with blue showing low local misorientation, and yellow/green showing high local misorientation. Local misorientations shown with 5° cutoff. Mapping step size is 0.6 μm. (Follow online version for clear and color picture) [108].

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7Conclusions

Considerable enhancement of research activity in ratcheting during the past three decades has been highlighted in this review. Among the various cyclic deformation mechanisms such as ratcheting, HCF, LCF and mean stress relaxation, ratcheting has the highest detrimental effect on the performance of an engineering component exposed to cyclic loading. The most detrimental damaging mechanism in cyclic loading is the superimposition of two simultaneous damage processes, namely, the progressive directional permanent strain accumulation and the fatigue damage due to continuous stress-strain hysteresis loop formation. The key motivation of this work stems from the complex damaging nature of ratcheting, which poses enormous challenge to design of safe engineering structure. After a comprehensive summary of the historical experimental activities on ratcheting since 1911, a review of the relations between the microstructural evolution and the ratcheting response in specimen and component level is presented. The current work focusing on the effect of stress levels, stress rate, temperature, planar anisotropy, previous loading history, multiaxial loading paths, ratcheting-tensile, tensile-ratcheting, ratcheting-low cycle fatigue, ratcheting-ratcheting and ratcheting-creep interactions. This comprehensive information explains why ratcheting is presently a topic of engineering research. The following conclusions can be made based on reported review works:

  • The ratcheting curve (ratcheting strain versus number of cycles plot) in engineering stress controlled ratcheting experimentation can be divided into primary, secondary and tertiary regions. Cyclic hardening of the material dominates in the primary region and softening due to reduction in cross sectional dominates in the tertiary region, while cyclic hardening and softening cancel out each other in the secondary region leading to a constant ratcheting rate.

  • The ratcheting strain accumulation direction is identical to the mean stress direction for uniaxial/proportional loading.

  • The ratcheting strain evolution is reversible in nature. In other words, tensile ratcheting strain accumulation caused by asymmetric stress cycling with tensile mean stress can be recovered during compressive ratcheting strain accumulation by asymmetric stress cycling with compressive mean stress. However, this does not imply that the ratcheting damage is reversible in nature.

  • The ratcheting life reduces and ratcheting strain accumulation rate increases with an increase in stress amplitude at constant mean stress or an increase in mean stress at constant stress amplitude.

  • The ratcheting life improves and ratcheting strain accumulation rate decreases with an increase in stress rate.

  • Ratcheting response is influenced by the planar anisotropy of the material i.e. texture of the material. For instance, IF steel has poor ratcheting resistance in 45° to rolling direction, whereas superior ratcheting resistance in the rolling direction. However, a material with other texture may exhibit different ratcheting response with various angles to the rolling direction.

  • Loading history of materials affects subsequent ratcheting response of the material. Monotonic pre-stressing alters initial ratcheting response, however with cycling, the ratcheting response is directed towards materials stable ratcheting response without load history effect. Pre-cycling with lower loads has no prominent effect on subsequent ratcheting response with higher loads. However, pre-cycling with higher loads has a considerable effect on subsequent ratcheting performance with lower loads, e.g. the ratcheting strain accumulation completely ceases/reduces and ratcheting life improves in the second step i.e. ratcheting with lower loads.

  • Ratcheting is a cyclic plastic deformation phenomenon; as a result, it depends on the loading path. For same mean stress and comparable equivalent stress amplitudes, the ratcheting strain accumulation rates can vary with the different degree of non-proportionality of loading paths. The highest ratcheting strain accumulation is achieved in uniaxial ratcheting experiment.

  • True stress amplitude and mean stress increase uncontrollably with increase in ratcheting strain build up during engineering stress/load controlled test. True stress controlled tests are favored to evade the area correction contradiction with the buildup of ratcheting strain.

  • Substantial variation in accumulated ratcheting strain and ratcheting life is observed between true and engineering stress controlled experiments. In true stress controlled test in the presence of tensile mean stress, an enhancement in ratcheting life and a lower accumulation of ratcheting strain is noticed in comparison with engineering stress controlled experiment. The opposite is true with compressive mean stress.

  • With the progression of ratcheting damage, yield stress and ultimate tensile stress increase and uniform elongation reduces.

  • Pre-ratcheting drastically reduces successive LCF life. Permanent ratcheting strain buildup is the primary reason for the reduction in LCF life. Pre-ratcheting alters the cyclic hardening/softening performance in following LCF experiments.

  • Ratcheting strain accumulation rate increases with increasing temperature.

  • Peak stress hold increases the ratcheting strain accumulation rate, while the peak stress hold effect is more effective at a higher temperature.

  • Ratcheting of carbon steel is qualitatively explained by the examined dislocation patterns and their progression. In the primary stage of ratcheting, dislocation density increases and the dislocation patterns such as dislocation veins and cells are gradually formed. The increase in dislocation density results in a rapid decrease in ratcheting strain accumulation rate. In the secondary stage of ratcheting, the dislocation density does not rise promptly and sub-grains are formed by the rearrangement of dislocations. Without alteration of dislocation density, ratcheting strain rate remains constant. The re-acceleration of ratcheting strain accumulation rate at the tertiary stage is generally caused by the fatigue crack initiation or gets closer to instability. This is a general observation; however the microstructural evolution may vary during ratcheting, depending upon the material and loading conditions.

  • Ratcheting specimens display much higher in-grain misorientations compared to LCF. Strain localization is detected at the ferrite/martensite interface in the soft ferrite phase for dual phase steel.

8Open areas for future research

Finally, regardless of the important work carried out on ratcheting to date, there are several inspiring and essential questions waiting to be addressed to improve our understanding on ratcheting in advanced materials and the safe engineering component design in this field of interest. The current knowledge on the topic illustrates that research efforts should be made especially in the following directions.

  • Only uniaxial true stress controlled ratcheting response is reported in the literature. Multiaxial true stress controlled ratcheting experimentation will be really challenging.

  • Observation of HCF-ratcheting, ratcheting-HCF and LCF-ratcheting interaction.

  • Little experimentation conducted on ratcheting response under 3D stress state, but more experimentation is required to understand the real life ratcheting phenomena.

  • More experimentation on microstructural evolution and correlation with the mechanical response of materials will be needed to understand the ratcheting and develop ratcheting resistant material.

  • For multiphase materials, how the applied stress/strain is partitioned among phases? The contribution of phases in ratcheting strain evolution is relatively unexplored.

  • Experimental investigation and microstructural correlation of ratcheting response of advance high strength steel (AHSS) and advance materials, where more than one deformation mechanisms are active.

  • Quantitative analysis of microstructural evolution during ratcheting and its use as an input to develop physics based constitutive model.

  • Establish relationships between microstructure evolution and specimen and/or component level ratcheting response.

Conflicts of interest

The authors declare no conflicts of interest.

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Surajit Kumar Paul completed his Ph.D from Jadavpur University, Kolkata, India in the year of 2012. He worked as a researcher at R&D, Tata Steel Limited, Jamshedpur for 3 years 11 months. After that he worked as an Alfred Deakin Post Doctoral Research Fellow at Deakin University, Victoria, Australia for 2 years. Then he worked as a Senior Scientist, Fatigue & Fracture group at CSIR- National Metallurgical Laboratory, Jamshedpur, India for a year. Currently he is working as an Assistant Professor, Department of Mechanical Engineering, Indian Institute of Technology Patna. Dr. Paul's has documented research output in the area of cyclic plasticity, sheet metal forming, high rate deformation, fatigue crack growth, multiaxial fatigue, continuum and multiphase micromechanics based finite element material modeling. He has published 56 research papers in peer reviewed international journals and number of national and international conference proceedings.

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