Cyclic Strain Accumulation Research Articles

In-vivo wear of hip surface replacements—a comparison of retrievals and simulator results

The wear of ultra-high molecular weight polyethylene (UHMWPE) has become a major focus regarding the long-term clinical performance of total joint replacements. Clinical retrieval analysis has revealed the existence of two distinct wear mechanisms that are operational in both total hip and total knee replacements. While the majority of the wear debris produced from the acetabular component is less than a micron in size and often particulate or fibrous in shape, much larger thin flakelike wear debris is produced from the tibial component. Two theoretical wear models that are based on the scale of intimate asperity interactions are proposed to account for the observed differences in hip and knee wear. Cyclic plastic strain accumulation is identified as the common cause for wear debris generation in both hip and knee replacements. In the case of acetabular cup wear, the scale of plastic deformation is limited to the sites of intimate micro-asperity contacts and the wear rate is defined by a critical strain criterion. In the case of tibial component wear, however, plastic deformation spreads into the subsurface to the site of macro-asperity contacts, and material can be removed by subsurface cracking and delamination. In both cases, the wear rate is strongly affected by the ultimate tensile strength and breaking elongation of the UHMWPE material.

Dwell Sensitive Fatigue Response of Titanium Alloys for Power Plant Applications

The phenomenon of “dwell sensitivity” in the α+β and near α titanium alloys and the intrinsic relationship with quasi-cleavage facet formation is discussed. In the present paper, particular emphasis is placed upon the role of “cold creep” and ambient temperature strain accumulation under cyclic loading. A process of stress redistribution between microstructurally distinct regions that demonstrate different strengths is proposed as the fundamental cause of facet development and subsequent dwell failures. A model to describe the redistribution process is validated through a matrix of fatigue testing designed to assess the effects of microstructural form, stress axiality, and periods of dwell loading at peak stress on cyclic strain accumulation.

Modeling of cyclic mobility in saturated cohesionless soils

Cyclic mobility is exhibited by saturated medium to dense cohesionless soils during liquefaction, due to soil skeleton dilation at large shear strain excursions. This volume-shear coupling mechanism results in phases of significant regain in soil shear stiffness and strength, and limits the magnitude of cyclic shear deformations. Motivated by experimental observations, a plasticity model is developed for capturing the characteristics of cyclic mobility. This model extends an existing multi-surface plasticity formulation with newly developed flow and hardening rules. The new flow rule allows for reproducing cyclic shear strain accumulation, and the subsequent dilative phases observed in liquefied soil response. The new hardening rule enhances numerical robustness and efficiency. A model calibration procedure is outlined, based on monotonic and cyclic laboratory sample test data.

The effect of dwell loading on the strain accumulation behavior of titanium alloys

The fatigue characteristics of titanium alloy IMI 834 were studied under both cyclic and dwell loading conditions. Strain data were taken from two different heat treatments of IMI 834 titanium alloy during fatigue cycling with 10 Hz haversine, 0.065, and 0.033 Hz trapezoidal loading wave forms. The resulting cyclic strain accumulation rates were calculated and compared to determine if a trend could be identified related to the significant reduction in life observed as a result of the dwell time at maximum load. It was found that, indeed, when high cyclic strain accumulation rates were observed, there was a significant reduction in fatigue life.

A two-dimensional model of cyclic strain accumulation in ultra-high molecular weight polyethylene knee replacements.

As new methods of sterilization of the ultra-high molecular weight polyethylene (UHMWPE) component in knee replacements are introduced, reported incidents of delamination will decrease. The prediction of plastic strain accumulation and associated failure mechanisms will then become more important in knee replacement design. The finite element analysis reported in this paper aims to advance the modelling of strain accumulation in UHMWPE over repeated gait cycles and seeks to determine the effects of the knee replacement design variables of geometry and kinematics. Material testing was performed under cyclic and creep conditions to generate the elastic, viscoplastic material model that has been used in this time-dependent analysis. Non-conforming geometries were found to accumulate plastic strains at higher rates than conforming geometries. The anatomical motion known as rollback initially produced lower strain rates, but predictions of the long-term response indicated that designs which allow rollback may produce higher strains than static designs after only about a week of loading for a knee replacement patient.

Thermal Fatigue of NiAl Single Crystals

ABSTRACTSingle crystals of [001]-oriented NiAI single crystals were subjected to thermal fatigue by a method which employs induction heating of disk-shaped specimens heated in an argon atmosphere. Several time-temperature heating and cooling profiles were used to produce different thermal strain histories in specimens cycled between 973 K and 1473 K. After thermal cycling, pronounced shape changes in the form of diametrical elongations along <100> directions with accompanying increases in thickness at and near the <100> specimen axes were observed. The deformations were analyzed in terms of operative slip systems in tension and compression, ratchetting (cyclic strain accumulation), and the elastic properties of NiAl. The experimental results correlate best with thermal stresses associated with the large elastic anisotropy of NiAl.

Response and cyclic strain accumulation of pressurized piping elbows under dynamic in-plane bending

Eight pairs of carbon and stainless steel, long and short radius welding elbows were tested under conditions of steady internal pressure and in-plane, resonant dynamic moments that simulated seismic excitations. The elbows had an outside diameter of 60.3 mm and thicknesses of 3.91 and 5.54 mm. The material properties are reported, and the testing procedure and experimental programme fully described. The dynamic response of the comonents indicates that the stainless steel elbows behave differently from the carbon steel elbows. The cyclic strain accumulation for each component is assessed and ratios of applied to limit moments of the elbows at onset of ratcheting are given for each material. While the gross deformation range increased with level of input in testing, no permanent overall swelling or ovalization was recorded; this is contrasted with similar results reported in the general literature.

Response and cyclic strain accumulation of pressurized piping elbows under dynamic out-of-plane bending

In a previous publication (1),† an experimental programme, involving four carbon and four stainless steel pairs of 2 inch NPS, 90° welding elbows tested under conditions of steady internal pressure and dynamic inputs that induced resonant in-plane bending at frequencies typical of seismic excitations, was described and some results reported. In this contribution, a similar test programme using identical pressurized components under dynamic conditions that induced out-of-plane external moments at similar frequencies is considered. For each material, two thicknesses (extra strong and standard weight specifications) were chosen and for each thickness two bend radius geometries (long and short) were tested. The similarities and differences in instrumentation, response and behaviour between the two programmes are highlighted. While the dynamic responses and the levels of moment achieved were similar for both types of external loads, there was an important difference in strain behaviour. Firstly, the direction of maximum strain was found to be at about 45° between the hoop and axial directions. Secondly, while there was practically no strain accumulation in the axial direction, ratcheting in both hoop and maximum principal strain directions was initiated at about the same level of input. Thirdly, the direction of highest ratcheting was found to be along the hoop direction rather than the direction of maximum principal strain. The cyclic strain accumulation against response moment for each component is assessed and ratios of applied to limit moment at onset of ratcheting are given for each material.

Wear mechanisms of UHMWPE in total joint replacements

The wear of ultra-high molecular weight polyethylene (UHMWPE) has become a major focus regarding the long-term clinical performance of total joint replacements. Clinical retrieval analysis has revealed the existence of two distinct wear mechanisms that are operational in both total hip and total knee replacements. While the majority of the wear debris produced from the acetabular component is less than a micron in size and often particulate or fibrous in shape, much larger thin flakelike wear debris is produced from the tibial component. Two theoretical wear models that are based on the scale of intimate asperity interactions are proposed to account for the observed differences in hip and knee wear. Cyclic plastic strain accumulation is identified as the common cause for wear debris generation in both hip and knee replacements. In the case of acetabular cup wear, the scale of plastic deformation is limited to the sites of intimate micro-asperity contacts and the wear rate is defined by a critical strain criterion. In the case of tibial component wear, however, plastic deformation spreads into the subsurface to the site of macro-asperity contacts, and material can be removed by subsurface cracking and delamination. In both cases, the wear rate is strongly affected by the ultimate tensile strength and breaking elongation of the UHMWPE material.

Stress state dependence of cyclic ratchetting behavior of two rail steels

Abstract Cumulative inelastic deformation or ratchetting occurs during cyclic loading in the presence of a mean stress. This problem has received considerable recent attention. The nonlinear kinematic hardening rule originally proposed by Armstrong and Frederick (AF rule) [1966] has been widely used for description of the overall character of hysteresis response during cyclic plasticity. However, this model generally overpredicts cyclic strain accumulation (ratchetting) under asymmetric loading with mean stress ( Bower [1987]; Bower & Johnson [1989]; Clement & Guionnet [1985]; Chaboche [1989,1991]; Chaboche & Nouailhas [1989]; McDowell & Lamar [1989]; McDowell [1992]). Moreover, unloading-reloading behavior associated with subcycle events under even uniaxial conditions ( Chaboche [1989]) are not adequately represented by the AF rule. The same comments apply to other nonlinear kinematic hardening rules of equivalent or similar nature such as bounding surface plasticity theory (cf. McDowell & Moyar [1991]). In this work, a modification of the dynamic recovery term of the AF rule is considered as recently proposed by Ohno and Wang [1991a,1991b]. The approach is established based on certain assumed crystalline slip system behavior and interaction between dislocation interactions at different size scales. Several important criteria are discussed for models capable of representing stress state and amplitude dependence of ratchetting behavior. Experimental results obtained on both a carbon rail steel and a heat-treated rail steel subjected to various uniaxial and nonproportional loading conditions are presented and correlated with an extension of the Ohno and Wang model, which accounts for a broader range of stress state and amplitude effects. An algorithm is developed to extrapolate the ratchetting rates obtained at relatively early cycles to very large numbers of cycles for test specimens. The method provides for dependence on the mean stress as well as amplitude of loading. The algorithm is applied to both carbon and heat-treated rail steels.

Stochastic Storm Profiles for Strain Accumulation in Clay

For offshore gravity platforms founded on clay, an important foundation failure mode arises from cumulative shear strain under cyclic loads. The major contribution to this cyclic strain accumulation comes from wave loads in sea states of high intensities. To analyze this and similar cumulative damage mechanisms, a probabilistic storm profile model is developed. Slepian random process models are used to estimate the temporal evolution of the significant wave height HS during a storm, during which HS exceeds a specified threshold. To predict storm profiles associated with any threshold, the model requires only conventional marginal wave statistics along with limited correlation information. Numerical results are shown for a North Sea location, where rare, high-threshold events can be verified by long hindcast histories. For an example foundation, predicted strain accumulation is compared with results from conventional storm profile models.

Effect of Laminate Orientation on the Thermomechanical Fatigue Behavior of a Titanium Matrix Composite

Thermomechanical fatigue (TMF) tests were conducted on the silicon carbide fiber and titanium alloy matrix composite, SCS-6/TIMETAL®21S. Three different laminate orientations were considered: [0]4, [0/90]s, and [0/±45/90]s. Both in-phase and out-of-phase stress-controlled tests were conducted under a temperature cycle of 150° to 650°C and a stress ratio of 0.1. The fatigue lives for these different orientations can be consolidated within a factor of 3 by normalizing the maximum applied stress (Smax) by the ultimate tensile strength at the Smax temperature of the TMF cycle. For all laminate orientations, the maximum and minimum strain increase during in-phase cycling, whereas only maximum strain increases during out-of-phase cycling. Damage accumulation under inphase cycling is attributed to a combination of the increasing stress carried by the [0] fibers due to cyclic matrix stress relaxation and the gradual breakage of [0] fibers. The damage during out-of-phase cycling is attributed to matrix cracks which initiate at the surface with the aid of the environment and/or initiate internally at the transverse fibers in [0/90]s and [0/±45/90]s composites. A simple model to compute cyclic strain accumulation based on the proposed mechanisms successfully captures the experimentally observed behavior. TMF life is shown to be sensitive to fiber volume fraction under inphase cycling, but not under out-of-phase cycling. TMF conditions are shown to be more severe than isothermal fatigue.

Structural changes of the Laves phase ErFe 2 during static and cyclic hydrogenation treatments

To investigate the structural changes of C15 Laves compound ErFe 2 during hydrogenation, which has a good potential as a hydrogen storage material, static and cyclic hydriding treatments were performed. During the static isothermal hydrogenation, an amorphous hydride phase is observed at about 200 °C without decomposition. From the variations in the charging conditions (temperature, time and pressure), it is found that amorphization is a thermally activated process and that some critical amounts of hydrogen atoms should be supplied to the matrix. Temperature-induced hydrogen absorption-desorption cycling results in a decrease in the reversible hydrogen content with increasing number of cycles. As a result of intrinsic degradation, amorphous or mixed ErH 2+Fe phases are formed. The thermal energy released during the hydriding reaction and the repetitive strain induce a phase decomposition. However, in the case of a smaller heat effect, the crystal structure is transformed to an amorphous state by the cyclic strain accumulation. Therefore, from the observed results, it is suggested that the amorphous phase is an intermediate and metastable phase formed during phase decomposition and that the corresponding reaction mechanism is closely related to the motion of the iron atoms. Also, amorphous phase formation is one of the possible degradation mechanisms of the metal hydrides during cyclic operation.

Effects of non-linear kinematic hardening on plastic deformation and residual stresses in rolling line contact

Existing methods for estimation of subsurface cyclic strain accumulation (ratchetting) and residual stresses in rolling contact are limited in applicability to a few cases of practical interest. Finite element solutions, for example, are potentially accurate but may only be employed for a small number of cycles for selected loading conditions and materials. This study concentrates on the estimation of cyclic plastic flow in rolling contact and associated residual stress development within the context of a set of simple constraints representative of plane strain line contact of cylinders. A reasonably sophisticated non-linear material constitutive law is employed. The behavior of two different rail steels is examined over a wide range of rolling contact conditions.

Damping, cyclic strain buildup and fatigue of rocks a generalized Ramberg-Osgood approach

A generalization of the Ramberg-Osgood model three dimensional cyclic loading was formulated for rocks in the previous paper [1] using discretized kinematic hardening concepts. Here, material functions are interpreted and calibrated. Perfect hysteresis, cyclic strain accumulation and fatigue are analyzed for typical loading histories.

Statistical consideration of plastic strain accumulation in cyclic deformation and fatigue crack initiation

Abstract : By considering a random nature of slip, we have obtained the elastic energy, stored in a slip region by cyclic deformation. It is similar, in form, to that given by Tanaka and Mura. Originator-supplied keywords include: Stochastics, fatigue, cyclic strain accumulation, Coffin-Manson Law, Reprints. (Author)

The role of an intracrustal asthenosphere on the behavior of major strike‐slip faults

Measurements of strain accumulation adjacent to the San Andreas fault indicate that the zone of strain accumulation extends only a few tens of kilometers away from the fault. Such a narrow zone of cyclic strain accumulation and release is consistent with the measured coseismic strain and inferred stress drop during the 1906 earthquake. The restricted zone of cyclic accumulation and release of elastic energy adjacent to major strike‐slip faults has been attributed to the damping effect of a viscoelastic asthenosphere. However, to explain the narrowness of the zone on the San Andreas fault, it is necessary to conclude that the thickness of the lithosphere is 10–20 km. This does not appear to be consistent with the relatively low surface heat flow measurements. In this paper an alternative four layer model is proposed to explain the behavior of the San Andreas fault. An upper elastic plate extends to a depth of about 15 km, the depth of the deepest seismicity on and adjacent to the fault. Beneath this upper elastic plate is a soft, intracrustal asthenosphere that exhibits a viscoelastic behavior. The viscous behavior of these crustal rocks at relatively low temperatures is attributed to either the presence of quartz, which is known to have a very soft rheology, or the presence of water that can lead to pressure solution creep or to both effects. Beneath this soft layer is a second elastic layer made up of the tough lower crustal and upper mantle rocks. And beneath this second elastic layer is the asthenosphere. There is extensive geological and geophysical evidence for the existence of an intracrustal asthenosphere both in California and elsewhere. We show that the damping due to the intracrustal asthenosphere can explain the observed narrow zone of cyclic strain accumulation and release on the San Andreas fault.

Endochronic inelasticity and incremental plasticity

Endochronic and non-associated plastic formulations are compared by introducing an “inelastic stiffness locus”, defined as the locus of all strain increments in the strain space which give the same magnitude of inelastic strain increments. For classical plasticity the locus is a straight line, while for endochronic formulations it is a circle, sphere or a quadratic surface (ellipsoid). Similarly to vertex hardening models and the deformation theory of plasticity, endochronic theory gives inelastic strain for strain increments tangential to the current loading surface, while plasticity gives perfectly elastic response. However, in contrast to vertex hardening, the endochronic inelastic strain for tangential strain increments is normal to the loading surface. Consequently, endochronic theory is stiffer than vertex hardening for this loading direction and is less prone to indicate instability. However, it is softer than plasticity. Among all possible constitutive relations, plasticity (without yield vertex) is least prone to indicate material instability, and so it is the least safe model to assume if test data are inconclusive as far as the type of constitution law is concerned.Tangential linearization of the endochronic inelasticity is presented. The tensor of tangential moduli, with all of its components, depends continuously on the strain increment direction in the strain space. Endochronic analogs of the loading surface and of kinematic and isotropic hardening rules are indicated, and stress-induced anisotropy of the quadratic form defining intrinsic time increments is formulated. It is shown that for proportional loading an endochronic formulation can be readily converted to an equivalent plasticity formulation. The fracturing material theory in which the loading function depends on strain rather than stress is also analyzed and it is shown that its inelastic stiffness locus is similar as for plasticity.Implications for material instability, and especially for stability of the response to pulsating loads of small amplitude, are discussed. By contrast to plasticity, but similarly to viscoplasticity, the endochronic inelasticity violates Liapunov-type stability conditions, but it meets a proper continuity condition. Refinements to satisfy both are possible, but questionable if one deals with materials such as geological materials, which are unstable or exhibit strain softening. Introducing unloading and reloading criteria and a certain type of kinematic hardening, the endochronic formulation may be refined so as to model cyclic strain accumulation yet satisfy Drucker's postulate for the hysteresis loops.

Plastic Buckling of Shells Under Cyclic Loading

The effects of cyclic strain accumulation or cyclic creep on the stability of thin cylindrical shells subjected to various combinations of repeated axial loading and repeated lateral pressure are examined. A constitutive model is employed to describe cyclic strain accumulation in geometrically-perfect cylindrical shells under uniform distributions of stress and the critical states of stress for elastic-plastic buckling or bifurcation-of-equilibrium are then established for such shells under combined axial compression and external pressure. Subsequent analyses for the cases of repeated lateral pressure and cyclic hydrostatic pressure suggest that strain accumulation can have a progressive destabilizing effect so that buckling may eventually occur after a certain number of cycles of loading.

A Plasticity Model for Cyclic Strain Accumulation

A general plasticity model is developed which is able to predict a cyclic strain accumulation phenomenon, sometimes called cyclic creep. To assess the consequences of the phenomenon for nonhomogeneous stress states, simple forms of the model are used in the analysis of two idealized structural elements. Very large stresses are found to develop for continued load cycling.