Cyclic Stress Relaxation Research Articles

Relaxation of residual stress in welded plates during long life fatigue loading

The presence of residual stress in welded components can have a significant impact on fatigue response. Residual stresses were assessed in thick welded A36 cantilever specimens (T-specimens) at the fatigue critical area. Testing involved subjecting the T-specimens to varying bending stresses and load cycles, leading to different levels of local plasticity at the weldtoe. Extensive X-ray diffraction (XRD) measurements were conducted to analyze the residual stress distribution near the weldtoe. Residual stress states were evaluated in both as-welded specimens and those subjected to fatigue loading with strain amplitudes up to 0.001 at the weldtoe stress concentration zone. The findings suggest that fatigue loading can induce changes in the welding-induced residual stress field, ranging from moderate to significant alterations. Therefore, fatigue life predictions should consider the potential evolution of residual stresses due to cyclic loading, including the effects of cyclic stress relaxation in fatigue life calculations.

Establishment of a Biaxial Testing System for Characterization of Right Ventricle Viscoelasticity Under Physiological Loadings.

Prior studies have indicated an impact of cardiac muscle viscoelasticity on systolic and diastolic functions. However, the studies of ventricular free wall viscoelasticity, particularly for that of right ventricles (RV), are limited. Moreover, investigations on ventricular passive viscoelasticity have been restricted to large animals and there is a lack of data on rodent species. To fill this knowledge gap, this study aims to develop a biaxial tester that induces high-speed physiological deformations to characterize the passive viscoelasticity of rat RVs. The biaxial testing system was fabricated so that planar deformation of rat ventricle tissues at physiological strain rates was possible. The testing system was validated using isotropic polydimethylsiloxane (PDMS) sheets. Next, viscoelastic measurements were performed in healthy rat RV free walls by equibiaxial cyclic sinusoidal loadings and stress relaxation. The biaxial tester's consistency, accuracy, and stability was confirmed from the PDMS samples measurements. Moreover, significant viscoelastic alterations of the RV were found between sub-physiological (0.1Hz) and physiological frequencies (1-8Hz). From hysteresis loop analysis, we found as the frequency increased, the elasticity and viscosity were increased in both directions. Interestingly, the ratio of storage energy to dissipated energy (Wd/Ws) remained constant at 0.1-5Hz. We did not observe marked differences in healthy RV viscoelasticity between longitudinal and circumferential directions. This work provides a new experimental tool to quantify the passive, biaxial viscoelasticity of ventricle free walls in both small and large animals. The dynamic mechanical tests showed frequency-dependent elastic and viscous behaviors of healthy rat RVs. But the ratio of dissipated energy to stored energy was maintained between frequencies. These findings offer novel baseline information on the passive viscoelasticity of healthy RVs in adult rats.

Anisotropic strain hardening in an extruded lean Mg-Al-Ca-Mn alloy

Compared to commercial magnesium (Mg) alloys, recently the low-alloyed Mg alloys have attracted extensive research interest for their advantages in formability, corrosion resistance, and low cost. However, their strain hardening behavior is yet fully understood. In this work, the strain hardening of an extruded lean Mg-Al-Ca-Mn alloy is qualitatively and quantitatively analyzed. As compared to the dislocation-dominated deformation along the extrusion direction (ED), the hardening along the transverse direction (TD) is significantly improved due to the activation of twinning. We quantified the specific contributions of twinning and dislocations to the net hardening effect through cyclic stress relaxation and calculations. Interestingly, the dominant hardening mechanism is always related to dislocations, even though the twin volume faction reaches ∼40 %. This work furthers our understanding of the deformation behavior of lean Mg alloys and indicates that the strain hardening of Mg alloys can be improved if the twin morphology is properly controlled.

The balance between work hardening and softening behaviors of Mg-xZn-1Gd-0.2Ca-0.1Zr alloys influenced by trace Zn addition

In the present work, the effect of adding trace amounts of Zn element on the microstructure, mechanical properties, work hardening and softening behaviors of Mg-xZn-1Gd-0.2Ca-0.1Zr alloys (ZGX) (x = 1, 2, 3 wt%) were systematically investigated. With the decrease in Zn content, the static recrystallized rate of as-annealed ZGX alloys gradually increased and recrystallized grain size decreased. Besides, a decrease in Zn content inhibited the generation of large secondary phases but promoted the formation of finely dispersed secondary phases. The tensile tests of as-annealed ZGX alloys showed that the lower the Zn content, the greater the yield point elongation (YPE) and yield stress, mainly attributed to the hindrance of grain boundaries to dislocations. The work hardening rate of as-annealed ZGX alloy with high Zn content was higher than that of as-annealed ZGX alloy with low Zn content. At the same time, cyclic stress relaxation tests indicated that as-annealed ZGX alloy with high Zn content was easier to soften. The increase in Zn content broke the balance between work hardening and softening of as-annealed ZGX alloys, mainly reflected in the rapid reduction of stress for ZGX alloy with high Zn content during the loading process, which can be ascribed to the accumulated dislocations detached from the pinning of the grain boundary and the second phases. These results provided a reference for the follow-up study of the mechanical properties of Mg alloys.

Local MIL-HDBK-5D equivalent stress based fatigue assessment of the gusset welded joint improved by Portable Pneumatic Needle-Peening treatment

This study proposes a local MIL-HDBK-5D equivalent stress (LMES) based approach to investigate the fatigue lives of Portable Pneumatic Needle-Peening (PPP) treated gusset welded joints made of SM490. The LMES range is identified by the elastic–plastic local stress cycle simulated by the muti-process finite element analysis, including welding, PPP, and fatigue loading processes. Using the LMES, Fatigue test results of as-welded (AW) and PPP treated joints are consolidated into a single S-N curve. This LMES based S-N curve can be used for evaluating fatigue life comprising the influence of residual stress, cyclic stress relaxation, and local weld toe geometry for welded joints studied in this work.

A Visco-Hyperelastic Constitutive Model to Characterize the Stress-Softening Behavior of Ethylene Propylene Diene Monomer Rubber.

Uniaxial and biaxial cyclic tensile tests and stress relaxation tests were performed on the ethylene propylene diene monomer (EPDM) material to investigate its stress-softening effect. The experimental results reveal that the EPDM material presents a significant Mullins effect during the cyclic stretching processes. Furthermore, it is found that the deformation of the EPDM material does not return to zero simultaneously with the stress, due to the viscoelasticity of the EPDM material. Therefore, this study combines pseudo-elasticity theory and viscoelastic theory to propose a visco-hyperelastic constitutive model. The proposed model is used to fit and analyze the uniaxial and biaxial cyclic test results of EPDM and a comparison is conducted with the corresponding hyper-elastic constitutive model. The results show that the proposed model is in good agreement with the experimental data and superior to the hyper-elastic constitutive model, especially when it comes to the stress-softening unloading process. This work is conducive to accurately characterizing the stress-softening behavior of rubber-like materials at large deformation and can provide some theoretical guidance for their widespread application in industry.

Crystal plasticity constitutive model and thermodynamics informed creep-fatigue life prediction model for Ni-based single crystal superalloy

Ni-based single crystal superalloys are the main constituent materials for aeroengine turbine blades. They are subjected to extensive in-service plastic deformation and creep-fatigue interaction, which can cause damage and failure and hence limit the turbine blade durability. In this study, a novel crystal plasticity-based constitutive model is proposed to predict the cyclic inelastic deformation of Ni-based single crystal superalloy under creep-fatigue loads, and the key aspects examined include cyclic strain hardening, ratcheting and stress relaxation behavior. The novelty of the model lies in the introduction of a dislocation density parameter in the kinematic hardening rule to describe the evolutionary characteristics of hysteresis loops. The constitutive model is implemented via the crystal plasticity finite element method and the predictions are in good agreement with experimental results. Furthermore, thermodynamic entropy generation is innovatively adopted as an indicator parameter for analysis of Ni-based single crystal creep-fatigue failure, and the corresponding creep and fatigue damage models are developed to evaluate the degree of damage. The half-life concept associated with the steady-state hysteresis loop is employed in the failure model to predict the creep-fatigue life without being limited by the computational efficiency of the crystal plasticity finite element method. The proposed model can well capture the characteristics of Ni-based single crystal creep-fatigue life, and the prediction falls within a scatter band of factor 2.0 compared to experimental results. The proposed creep-fatigue life prediction model is underpinned by deformation and failure mechanisms, which would provide a basis for accurate analysis and robust assessment of Ni-based single crystal superalloy performance and life.

Low-cycle fatigue behaviour of hot-rolled titanium-clad bimetallic steel

Titanium-clad (TC) bimetallic steel is able to integrate the superior corrosion resistance of titanium alloy into traditional corrosion-susceptible structural steels, producing prominent life-cycle safety, serviceability and durability. Nevertheless, the relevant seismic performance and fatigue behaviour reported in existing literature are still limited and insufficient to support the codification for structural design of such advanced steel. In order to develop proper plastic/seismic design methodology for TC bimetallic steel structure, the cyclic behaviours and low-cycle fatigue life prediction of such metal must be thoroughly investigated. This paper aims to study the low-cycle fatigue behaviour of hot-rolled bonded TC bimetallic steel manufactured from TA2 titanium alloy and Q355B structural steel. The strain amplitude of low-cycle fatigue (LCF) test ranges from 0.5% to 2.5%, and the strain ratio applied herein includes 0 and -1. The experimental phenomenon, LCF failure mechanism, cyclic stress-strain relationship of different tests are thoroughly compared and discussed. Besides, the influence of strain rate and bond strength are simultaneously demonstrated. The LCF life are fitted and validated through Basquin-Coffin-Manson model, Kuroda model and energy method, respectively. The research outcomes demonstrate that the LCF cracks of TC bimetallic steel tend to be initiated at the cladding layer and propagated into the substrate layer due to a coupled buckling-fatigue failure mechanism. Several representative fatigue behaviour of conventional mild (CM) steels including the three-stage cyclic softening and mean stress relaxation have not been observed in this experimental study. The strain rate exhibits distinct influence on the LCF life and failure mechanism. Both Basquin-Coffin-Manson model and energy method can provide more favourable prediction accuracy for LCF life of TC bimetallic steel than the Kuroda model. Generally the LCF life of TC bimetallic steel is shorter than that of structural steels, stainless steels, titanium alloys and stainless-clad (SC) bimetallic steels. The test records and fatigue-life model parameters obtained can lay a solid foundation for seismic analysis and damage evaluation of TC bimetallic steel structure.

A physically-based constitutive model for a novel heat resistant martensitic steel under different cyclic loading modes: Microstructural strengthening mechanisms

Cyclic responses of a novel heat resistant martensitic steel, 9Cr3Co3W1CuVNbB steel, under different loading modes were studied to reveal its complex strengthening mechanisms at high temperature. Based on the experimental observations, dislocation strengthening, precipitation strengthening by M23C6 phase, MX phase, and Cu-rich phase, and subgrain boundary strengthening were the main mechanisms for its excellent fatigue and creep-fatigue properties. In particular, the dynamic process of interaction between phase and dislocation were studied with the help of molecular dynamics method, and the different contributions of hard and soft phases in the studied steel were determined in fatigue and creep-fatigue loading. Based on these phenomena, a physically-based constitutive model was proposed for both fatigue and creep-fatigue (dwell fatigue at elevated temperature) tests considering various micromechanical mechanisms. Three ways for dislocation annihilation were proposed to simulate the dislocation evolution under different loadings. In addition, the effect of Cu-rich phase was modeled by critical breaking angle and dislocation line tension. The capability of the proposed model under different loading modes was verified by comparing cyclic responses, hysteresis loops, stress relaxation, and dislocation density evolution. The proposed model provides an alternative perspective on understanding fatigue and creep-fatigue behaviors of heat resistant martensitic steels owning the similar strengthening mechanisms.

Mechanical behavior of adhesively bonded butt‐joints under cyclic loading: Experiments and constitutive model

AbstractThe cyclic loading experiments on HP‐172B sealant bonded tubular butt‐joints were carried out with the strain‐controlled mode, and the effects of strain amplitude and mean strain on the cyclic relaxation stress and cyclic softening variable of the bonded butt‐joint were investigated. The experimental results show that the stress–strain response curve of the butt‐joint presents a corrugated shape under cyclic loading. The cyclic stress relaxation and cyclic softening of the bonded butt‐joint occur. The increase of mean strain and strain amplitude intensifies the cyclic stress relaxation and cyclic softening behaviors. According to the experimental observation, a nonlinear viscoelastic model is proposed to predict the mechanical behavior of butt‐joints under cyclic loading, which considers the cyclic stress relaxation and cyclic softening of the bonded butt‐joint. The comparisons between the model calculation and the experimental data show that the calculated stress–strain curve is in good agreement with the experimental data.

A comparison on isothermal and thermomechanical fatigue behavior of 316LN stainless steel with various tension dwell time

Isothermal and thermomechanical fatigue tests with various tension dwell time (designated as creep-IF and creep-TMF respectively) were conducted. The cyclic stress response and stress relaxation behavior were qualitatively and quantitatively discussed based on TEM and EBSD characterization. The fatigue dominated transgranular crack initiation and propagation led to specimen fracture in all creep-IF tests. The transition of dominant damage mechanism from fatigue to creep-fatigue interaction occurred when dwell time increased to 1800 s in creep-TMF test, which caused the intergranular fracture mode and a much shorter life than creep-IF. Moreover, the life prediction model based on tension strain energy was proposed.

Impact of Moisture Content on the Elasto-Viscoplastic Behaviour of Rammed Earth Wall: New Findings

The influence of hydric state on the elasto-viscoplastic behaviour of a unstabilised rammed earth (URE) wall has yet to be studied in the literature. This paper presents an experimental campaign on a rammed earth wall. The aim is to evaluate the link between the mechanical properties (including viscosity) and the varying hydric state inside the drying wall after manufacture. Cyclic axial compression and stress relaxation tests were carried out for this purpose. A compression test was conducted up to 0.1 MPa, followed by a stress relaxation test. These tests were periodically performed over 32 weeks. In addition, the hydric state inside the wall was monitored by humidity sensors. The results show that both the elastic modulus and the dynamic viscosity coefficient increase as the structure dries. A dependence of the mechanical behaviour on time is therefore found in these samples in the transient state. This can occur when the sample is in the drying or wetting phase. As rammed earth is a material particularly sensitive to water, this result is crucial for the durability of earthen constructions.

Time-dependent hyper-viscoelastic parameter identification of human articular cartilage and substitute materials

Numerical simulations are a valuable tool to understand which processes during mechanical stimulations of hydrogels for cartilage replacement influence the behavior of chondrocytes and contribute to the success or failure of these materials as implants. Such simulations critically rely on the correct prediction of the material response through appropriate material models and corresponding parameters. In this study, we identify hyper-viscoelastic material parameters for numerical simulations in COMSOL Multiphysics® v. 5.6 for human articular cartilage and two replacement materials, the commercially available ChondroFillerliquid and oxidized alginate gelatin (ADA-GEL) hydrogels. We incorporate the realistic experimental boundary conditions into an inverse parameter identification scheme based on data from multiple loading modes simultaneously, including cyclic compression-tension and stress relaxation experiments. We provide individual parameter sets for the unconditioned and conditioned responses and discuss how viscoelastic effects are related to the materials’ microstructure. ADA-GEL and ChondroFillerliquid exhibit faster stress relaxation than cartilage with lower relaxation time constants, while cartilage has the largest viscoelastic stress contribution. The elastic response predominates in ADA-GEL and ChondroFillerliquid, while the viscoelastic response predominates in cartilage. These results will help to simulate mechanical stimulations, support the development of suitable materials with distinct mechanical properties in the future and provide parameters and insight into the time-dependent material behavior of human articular cartilage.

Non-local continuum damage model for poro-viscoelastic porous media

We present a novel poro-damage-viscoelastic model for predicting the failure response of fluid-saturated porous geomaterials. The Generalized Maxwell model is introduced for the representation of the viscoelastic behavior of the solid skeleton, which is achieved by a standard Prony-series type expansion. Damage regularization is obtained by an non-local integral-type formulation and damage behavior is described by Mazars model with the modified von Mises-type equivalent strain measure. The poromechanics parameters (Biot’s coefficient, Biot’s modulus) are functions of damage, and the fluid flow obeys Darcy’s seepage law in the entire domain, while the permeability is assumed to be anisotropic and strain dependent. The coupled system is discretized in time using a backward Euler scheme. The non-linear system is linearized using a Newton Raphson scheme and solved monolithically every time step. A consistent Jacobian matrix and residual vector are derived analytically. Several numerical examples are studied in order to investigate the performance of the proposed approach, including (i) a column undergoing hysteresis from cyclic loading, stress relaxation, creep and variable strain rate loading tests and (ii) fluid-driven fracturing in a 2D poro-viscoelastic domain. The numerical time-dependent results exhibit mesh insensitivity for all field variables, and confirm the feasibility and applicability of the proposed non-local damage model for simulating hydraulic fracture. • A non-local damage model for poro-viscoelastic saturated porous media is proposed. • Von-Mises strain measure is used to drive the non-local integral type damage growth. • Damage-response includes nonlinear Biot’s coefficients and anisotropic permeability. • A mixed FEM solution is developed, including a monolithic iterative solution. • Analytically derived Jacobian is used to drive the non-linear solution of equations. • Benchmark problems include poro-viscoelastic column and hydraulic fracture problems. • Objective mesh-independent and oscillation free numerical results are presented. • The model has the potential to represent time-dependent damage in several rock types.

Experimental and theoretical investigation on mechanical behaviors of TB991 weld sealant under cyclic loading

AbstractThe mechanical behaviors of TB991 weld sealant under cyclic loading conditions were experimentally investigated. The evolution of relaxation stress, cyclic softening, and dissipated energy was evaluated with the effect of strain amplitude and mean strain. The experimental results showed that the stress–strain response curves of the first loading‐unloading and cyclic loading‐unloading were significantly different. The phenomenon of stress relaxation and cyclic softening occurred under cyclic strain loading conditions. Furthermore, the relaxation stress and dissipated energy decreased rapidly during the initial cyclic loading and then steadily decreased with the increase of cycle number, while the cyclic softening increased rapidly at first and then steadily. Besides, a viscoelastic constitutive model was proposed which can describe the different shapes of stress–strain curve between the initial loading‐unloading and the cyclic loading‐unloading and also considers the cyclic stress relaxation and cyclic softening of the materials under cyclic loading condition. Comparisons between the numerical results and the experimental data demonstrated that the proposed model can better describe the mechanical behavior of TB991 weld sealant under cyclic loading conditions.

Effect of cyclic softening and mean stress relaxation on fatigue crack initiation in a hemispherical notch

AbstractCorroded surfaces of offshore mooring chains typically show a very irregular shape with different pit geometries. Fatigue tests were performed in three‐point bending on specimens with hemispherical notches, representing an idealized geometry of a corrosion pit. Digital image correlation was used to detect crack initiation lives and locations. The aim of the study was to quantify mean stress relaxation (MSR) and its influence on fatigue initiation life. MSR data were obtained from strain‐controlled fatigue tests on R4‐grade offshore mooring chain steel. Interestingly, MSR was observed even at a stress amplitude below the cyclic yield stress. For initiation lives below 100,000 cycles, significant improvement in predictions was obtained if cyclic softening and MSR were accounted for. Using only the monotonic stress‐strain curve led to less accurate predictions. For longer lives, scatter in the base material data and residual stresses from machining of the notch made predictions less accurate.

Analysis of strain hardening behavior of a high-Mn TWIP steel using electron microscopy and cyclic stress relaxation

Electron microscopy and cyclic stress relaxation experiments were employed to study the dislocation-obstacle interactions and activated hardening mechanisms, during tensile straining of a high-Mn TWIP steel specimen, and to estimate the contributions of hardening mechanisms to the strain hardening behavior. Electron contrast channeling and high-resolution electron backscattered diffraction images showed that deformation twins and their twin boundaries affect the dislocation evolutions inside both the matrix and twin lamellae. High-resolution transmission electron microscopy suggested that twin boundaries (TBs) can be passed by dislocations through the dislocation multiplication mechanism resulting in the nucleation of sessile dislocations and alternated stacking faults at TBs. Consequently, high dislocation density was developed behind the TBs resulting in enhancement of the strain hardening rate through the composite hardening effect. Various thermally activated parameters determined through cyclic stress relaxation tests indicated that dislocation evolution, developed by TBs in terms of the composite effect, was the prevalent rate-controlling mechanism, imparting higher strengthening than TBs in terms of the dynamic Hall–Petch effect. Finally, the high nucleation tendency of Shockley partial dislocations at TBs was interpreted from the variation of the stress exponent and independent plastic strain rate, and also from the general stacking fault energy point of view.

A modified damage-coupled viscoplastic constitutive model for capturing the asymmetric behavior of a nickel-based superalloy under wide creep-fatigue loadings

In this study, cyclic deformation behaviors of nickel-based GH4169 superalloy are investigated in both experimental and simulated aspects via cyclic loading waveforms (i.e., PP, CP, PC and CC) at 650℃. Cyclic softening, stress relaxation and damage evolutions are analyzed, in which asymmetric cyclic softening in both peak/valley directions are demonstrated. The analysis of internal stress evolutions indicates that back stress is dominant and isotropic stress is secondary in cyclic softening. Afterward, a modified damage-coupled viscoplastic constitutive model is established to describe the complex cyclic behaviors as well as the damage evolutions. A term related to the first invariant of stress is incorporated into isotropic hardening rule and a softening factor introduced into the Ohno-Wang kinematic hardening rule. Additionally, a damage variable related to Young’s modulus is coupled into the model, which is experimentally validated via life prediction for more abundant experimental data points. The modified model is expected to provide an in-depth insight into cyclic behaviors and fatigue life under wide loading waveforms for industrial applications.

Polymerization-Induced Self-Assembly Toward Micelle-Crosslinked Tough and Ultrastretchable Hydrogels

As a promising class of tough and ultrastretchable hydrogels, micelle-crosslinked hydrogels have been restrained by the scarcity of micellar crosslinkers with a high concentration, controlled nanostructure, and uniform size distribution. Herein, polymerization-induced self-assembly (PISA) was demonstrated to be a general and powerful platform for micellar crosslinkers, affording micelle-crosslinked hydrogels with tailorable chemical structures, mechanics, and functionality. Poly(N,N-dimethylacrylamide)-b-poly(diacetone acrylamide) (PDMAc-b-PDAAM) micellar crosslinkers with a controlled nanostructure and uniform size distribution were prepared via PISA and one-step post-polymerization modification at high concentrations. Copolymerization of these micellar crosslinkers with acrylamide generated tough and ultrastretchable hydrogels, whose mechanical properties were found correlated with the concentration, nanostructure, and chemical composition of the micelles. The energy dissipation mechanism of these micelle-crosslinked hydrogels was analyzed via cyclic mechanical tests and stress relaxation experiments. The general feasibility of PISA toward micelle-crosslinked hydrogels was verified by systematic evaluation of both aqueous (including 2-methoxyethyl acrylate, tetrahydro-2-furanylmethyl acrylate, and 4-hydroxybutyl acrylate) and alcoholic (including benzyl methacrylate, lauryl methacrylate, styrene, and benzyl acrylate) PISA formulations, producing hydrogels with diverse chemical structures, mechanics, and functionalities depending on the micellar crosslinkers. The modularity of this strategy was further demonstrated by the fabrication of fluoro-functionalized hydrogels with fluoro-containing micellar crosslinkers. This strategy has significantly enlarged the scope and application of micelle-crosslinked hydrogels.

Effect of cyclic straining with various rates on stress softening/hysteresis and structural evolution of filled rubber: A time-resolved SANS study

The effect of cyclic straining on stress softening/hysteresis and structural evolution silica filled deuterated silicone rubber (SFdSR) during cyclic deformation has been investigated. In situ rheo-small-angle neutron scattering (Rheo-SANS) measurements were conducted with engineering strain rates (έ) spanning from 0.001 to 0.1 s−1. Moreover, superimposed time-resolved SANS technique is utilized. The non-linear behaviors all exhibit strong έ and cycle-number (No.C) dependency. Rheo-SANS suggests that the orientation of bound rubber responses sensitively to the strain, έ, and No.C, which presents an accumulative characteristic, associated with cyclic stress relaxation of the engineering stress-nominal strain curves. All the results consistently suggest that some substantial permanent changes occur within bound rubber, filler network, and rubber matrix after deforming the samples of virgin state. Evolutions would drastically develop during the initial couple of cycles, then accumulate and reach to a newly established equilibrium under constant έ, as long as the maximum strain is not exceeded.