Uniaxial ratcheting and failure behaviors of two steels

The strain cyclic characteristics, ratcheting and failure behaviors of 25CDV4.11 steel and SS304 stainless steel were experimentally studied under uniaxial cyclic tests and at room temperature. The cyclic hardening/softening features of the materials were first observed under uniaxial strain cycling; and then the ratcheting and failure behaviors of the materials were researched in detail under cyclic stressing. The effects of stress amplitude and mean stress on the ratcheting and failure were discussed under uniaxial asymmetrical stress cycling. It is concluded that the ratcheting and failure behaviors of the materials depend greatly on the cyclic softening/hardening features of the materials and the stress values of cyclic loading. Some conclusions useful to understand the fatigue failure of the materials presented under asymmetrical cyclic stressing are obtained.     

Modeling and characterization of cyclic relaxation and ratcheting using the distributed-element model

Constitutive modeling of cyclic relaxation and ratcheting (cumulative inelastic deformation) is developed on the basis of the distributed-element model (DEM). Although the original DEM is capable of describing general, elastic–plastic behavior for cyclically stabilized materials, it has the inadequacy of not being able to account for the effect of cyclic relaxation and ratcheting. By introducing the nonlinear kinematic hardening rule proposed by Armstrong and Frederick into element behavior of the DEM, the model becomes effective in characterizing the behavior of cyclic relaxation and ratcheting. Validation of the modified DEM is conducted by simulating cyclic behavior of various metal materials, including CS 1018, heat-treated rail steel, and Grade 60 steel. The results show that the modified DEM demonstrates realistic behavior of materials in both uniaxial and biaxial cyclic relaxation and ratcheting. Furthermore, detailed investigation of element behavior in the model provides us with additional insight into complex behavior and characteristics of materials in cyclic relaxation and ratcheting.     

Temperature-dependent ratcheting of PTFE gaskets under cyclic compressive loads with small stress amplitude

Uniaxial stress-controlled ratcheting experiments on PTFE gaskets under cyclic compressive loads with small stress amplitude were performed. The effect of temperature on the deformation behavior was considered. Results showed that the compressive modulus decreases rapidly when the temperature increases from 100 °C to 200 °C. Compressive ratcheting deformation with cycles increase significantly with the increases of temperature. The ratcheting deformations at 100 °C, 150 °C and 200 °C are nearly two, three and five times that at room temperature, respectively. Most of ratcheting deformation mainly occurs during the first 20 cycles because the subsequent ratcheting rate and strain range are small and much less than those in the previous cycles. The accumulated deformation under cyclic loads with small stress amplitude is relatively approach to the static compressive creep with the same peak stress. Therefore, the accumulated deformation with time of PTFE gaskets obtained by cyclic compression with small stress amplitude can be estimated by the corresponding static creep deformation with good accuracy under the approximate stress rate and the same temperature, especially at room temperature.     

Shakedown analysis of shape memory alloy structures

Phase transformational shakedown of a structure refers to a status that plastic strains cease developing after a finite number of loading cycles, and subsequently the structure undergoes only elastic deformation and alternating phase transformations with limited magnitudes. Due to the intrinsic complexity in the constitutive relations of shape memory alloys (SMA), there is as yet a lack of effective methods for modeling the mechanical responses of SMA structures, especially when they develop both phase transformation and plastic deformation. This paper is devoted to present an algorithm for analyzing shakedown of SMA structures subjected to cyclic or varying loads within specified domains. Based on the phase transformation and plastic yield criteria of von Mises-type and their associated flow rules, a simplified three-dimensional phenomenological constitutive model is first formulated accounting for different regimes of elastic–plastic deformation and phase transformation. Different responses possible for SMA bodies exposed to varying loads are discussed. The classical Melan shakedown theorem is extended to determine a lower bound of loads for transformational shakedown of SMA bodies without necessity of a step-by-step analysis along the loading history. Finally, a simple example is given to illustrate the application of the present theory as well as some basic features of shakedown of SMA structures. It is interesting to find that phase transformation may either increase or decrease the load-bearing capacity of a structure, depending upon its constitutive relations, geometries and the loading mode.     

Uniaxial ratcheting and fatigue failure of tempered 42CrMo steel: Damage evolution and damage-coupled visco-plastic constitutive model

Uniaxial ratcheting and fatigue failure of tempered 42CrMo steel were observed by the tests under the uniaxial stress-controlled cyclic loading with non-zero mean stress [G.Z. Kang, Y.J. Liu, Mater. Sci. Eng. A 472 (2008) 258–268]. Based on the obtained experimental results, the evolution features of whole-life ratcheting behavior and low-cycle fatigue (LCF) damage of the material were discussed first. Then, in the framework of unified visco-plasticity and continuum damage mechanics, a damage-coupled visco-plastic cyclic constitutive model was proposed to simulate the whole-life ratcheting and predict the fatigue failure life of the material presented in the uniaxial stress cycling with non-zero mean stress. In the proposed model, the damage was divided into two parts, i.e., elastic damage and plastic damage, which were described by the evolution equations with the same form but different constants, since the maximum applied stresses in most of loading cases were lower than the nominal yielding strength of the material. The ratcheting of the material was still described by employing a nonlinear kinematic hardening rule based on the Abdel-Karim–Ohno combined kinematic hardening model [M. Abdel Karim, N. Ohno, Int. J. Plast. 16 (2000) 225–240] but extended by considering the effect of damage. The maximum strain criterion combined with an elastic damage threshold was employed to determine the failure life of the material caused by two different failure modes, i.e., fatigue failure (caused by low-cycle fatigue due to plastic shakedown) and ductile failure (caused by large ratcheting strain). The simulated whole-life ratcheting behavior and predicted failure life of tempered 42CrMo steel are in a fairly good agreement with the experimental ones.     

Multiscale experimental investigations about the cyclic behavior of the 304L SS

This work follows a series of experiments carried out earlier at INSA of Rouen (Hassan, T., Taleb, L., Krishna, S., 2008. Influence of non-proportional loading paths on ratcheting responses and simulations by two recent cyclic plasticity models. Int. J. Plast. 24, 1863–1889). It investigates the elastoplastic cyclic behavior of a 304L stainless steel at room temperature. In a first step the cross path effect on ratcheting is confirmed, as well as the crucial role of the loading path non-proportionality. Strain controlled tests are also conducted for different strain amplitudes and loading paths. Cross-hardening effect appears more important when the shearing sequence is followed by the axial one. Moreover for alternating axial and shearing cycles, this phenomenon occurs after each crossing sequence leading to a very significant strain hardening, at least of the same order as the one obtained after a circular strain path. Yet, the magnitude of the observed over hardening does not necessarily seem a function of the cumulated plastic strain.     

An application of Curie’s principle to elastoplastic dynamics

This paper deals with the stability and the dynamics of a harmonically excited elastic–perfectly plastic unsymmetrical oscillator. Stability of the periodic orbits is analytically investigated with a perturbation approach. The occurrence of ratcheting effect is discussed for this system, and is related to the loss of symmetry of the periodic orbit in the phase space. Curie’s principle of symmetry is numerically verified for the symmetrical system with positive damping. Therefore, the observation of ratcheting phenomenon is necessarily associated to a breaking of symmetry in the constitutive behaviour, or in the forcing term. However, the generalized version of Curie’s principle has to be considered when a negative damping is introduced.     

Plastic ratcheting induced cracks in thin film structures

In the microelectronic and photonic industries, temperature cycling has long been used as a reliability test to qualify integrated materials structures of small feature sizes. The test is time consuming, and is a bottleneck for innovation. Tremendous needs exist to understand various failure modes in the integrated structures caused by cyclic temperatures. This paper presents a systematic study of a failure mechanism recently discovered by the authors. In a thin film structure comprising both ductile and brittle materials, the thermal expansion mismatch can cause the ductile material to plastically yield in every temperature cycle. Under certain circumstances, the plastic deformation ratchets, namely, accumulates in the same direction as the temperature cycles. The ratcheting deformation in the ductile material may build up stress in the brittle materials, leading to cracking. The paper introduces an analogy between ratcheting and viscous flow. An analytical model is developed, which explains the experimental observations, and allows one to design the structure to avert this failure mode. Design rules with increasing levels of sophistication are described. Concepts presented here are generic to related phenomena in thin film structures.     

Analytical elasto-creep model of interfacial thermal stresses and strains in trilayer assemblies

A two-dimensional model has been developed for thermal stresses, elastic strains, creep strains, and creep energy density at the interfaces of short and long trilayer assemblies under both plane stress and plane strain conditions. Both linear (viscous) and non-linear creep constitutive behavior under static and cyclic thermal loading can be modeled for all layers. Interfacial stresses and strains are approximated using a combination of exact elasticity solutions and elementary strength of materials theories. Partial differential equations are linearized through a simple finite difference discretization procedure. The approach is mathematically straightforward and can be extended to include plastic behavior and problems involving external loads and a variety of geometries. The model can provide input data for thermal fatigue life prediction in solder or adhesive joints. For a typical solder joint, it is demonstrated that the predicted cyclic stress–strain hysteresis shows shakedown and a rapid stabilization of the creep energy dissipation per cycle in agreement with the predictions of finite element analysis.     

Accelerated ratcheting testing of polycarbonate using the time-temperature-stress equivalence method

The long-term performance of polymers under cyclic loading is important for safety assessments in engineering applications. The deformation process under the cyclic loading can be accelerated through use of temperature and stress. As for asymmetric cyclic loading, so called ratcheting, a time-temperature-stress (TTS) equivalence method in which all the parameters have clear physical meanings and can be determined experimentally, was proposed to predict the long-term cyclic loading behavior for polycarbonate using short-term data. Taking into consideration the effects of both the mean stress and the stress amplitude, the ratcheting compliance was defined and its evolution function was also provided. Next, the TTS equivalence method was validated using the long-term ratcheting test results for the polycarbonate. Time, temperature, and stress do show equivalent effects on long-term ratcheting of polycarbonate. Using the proposed method, time and cost can be dramatically saved for the assessment of the long-term cyclic loading performance of polycarbonate.