Complex Stress Histories Research Articles

Thermo-Mechanical Deformation History and the Residual Stress Distribution in Cold Spray

In cold spray, high gas temperatures and high velocity impact of particles introduce complex thermal and stress histories in the coating layers and the substrate. It is crucial to understand the interplay between temperature evolution and residual stress development as the residual stresses could potentially cause distortion and/or delamination. In this study, a system-level cold-spray deposition model is developed. The model includes a moving heat source, material addition and thermo-mechanical stress analyses. The heat source model is first validated by qualitatively comparing the thermal history with experimental measurements from literature. The system-level model is then used to calculate the residual stresses and distortion in the cold-sprayed Cu/steel system. The influence of the spray path on the residual stress development is systematically analyzed. The corresponding interface residual stress states are also examined for the different spray paths. Simulation results indicate that the thermo-mechanical analysis using the developed system-level model can provide an effective way to assist in optimizing the cold-spray coating deposition strategy and improve the coating performance.

A kinematic hardening model based on endochronic theory for complex stress histories

While the field of soil constitutive modeling is rich, the availability of models that capture the behavior of different soil types under complex loading is limited. This study presents the development and validation of the Multi-Mechanical Model (MMM). The MMM is an elasto-plastic kinematic hardening model, which extends an earlier endochronic model by introducing the third stress invariant, accounts for shear-volumetric coupling in granular materials, and displays ratcheting behavior during stress reversals. A series of triaxial and isotropic consolidation tests are used to calibrate the MMM to materials found in conventional unbound granular materials and subgrades, such as crushed limestone, Leighton Buzzard sand, and Vicksburg Buckshot clay. The MMM is tested against resilient modulus test data that present complex stress histories. The study shows the MMM is straightforward in its calibration, while also displaying a robust capability in capturing the complex behaviors of the different soil types under various loading conditions. While positioned for applications in other areas, the MMM’s capabilities in capturing the short-term pore pressure response of fine-grained materials, the shear-induced volume change and stress-hardening effects of granular materials, and ratcheting behavior during repeated loading conditions make it well-suited for addressing pavement problems.

Process-oriented validation of hardening models in a cyclic bending test

Abstract In terms of forming processes with complex stress histories, like operations with drawbeads, the implementation of a kinematic hardening rule can significantly improve the numerical prediction quality. However, the variety of mathematical formulations and the non-standardized identification methodology make a preliminary evaluation of the models with respect to their subsequent application necessary. The use of a cyclic bending test is a very flexible and robust technique to validate material models. In view of the bending-like load distribution during a drawing operation of an open shape, this test allows a process near emulation of the forming history. Within this contribution, the realization of a defined strain history - derived form a deep drawing process with draw beads - is presented. For the high-strength steel HCT780X and the aluminum alloy AA6014-T4 an isotropic hardening rule as well as the extension with a kinematic hardening model according Chaboche and Rousselier are evaluated. The result’s transferability is finally analyzed on basis of the springback calculation of the deep drawing operation.

Simulating the effects of induced anisotropy on liquefaction potential using a new constitutive model

SUMMARY The effects of induced anisotropy on the undrained behaviour of very loose and saturated sands have been a subject of intensive investigation, both experimentally and theoretically, by several authors in the past few years. This paper proposes an original constitutive model well-adapted to simulate the behaviour of sands subject to complex stress histories, in particular, the preloading cycle along the classical drained stress path in compression. The developed model belongs to the family of critical state models. Its construction is based on a few theoretical concepts taken from the theory of ‘Bounding Surface Plasticity’ developed among others by Y. Dafalias and Popov (1975), the ‘Clay And Sand Model’ (CASM) of H. Yu (2006), the CJS model (B. Cambou and K. Jafari (1988)) and the hyperelastic isotropic model of P. Lade (1987). To accurately simulate volume changes, which represent a key element in soil behaviour, a state-dependent dilatancy rule is proposed, which can account for the influences of stress and void ratio. The current void ratio depends implicitly on the irreversible strains already accumulated hence the strain history. A kinematic hardening is combined with an isotropic hardening, involving rotation and distortion of the bounding surface, in order to capture correctly the experimental observations. Comparisons of experimental results to numerical simulations show that the model is able to simulate with a good precision the major trends of undrained responses of loose and presheared sands. It predicts correctly rapid static liquefaction at small or null drained preloading, as well as the progressive transition to a completely stable behaviour typical of dense sands, while the sample is loose in reality. At intermediate to large amplitudes of preloadings, the model also predicts correctly the temporary stage of instability when the deviatoric stress decreases slightly before rising up again. Copyright © 2013 John Wiley & Sons, Ltd.

Fatigue life assessment under a complex multiaxial load history: an approach based on damage mechanics

ABSTRACTIn order to assess the fatigue behaviour of structural components under a complex (cyclic or random) multiaxial stress history, methods based on damage mechanics concepts can be employed. In this paper, a model for fatigue damage evaluation in the case of an arbitrary multiaxial loading history is proposed by using an endurance function which allows us to determine the damage accumulation up to the final failure of the material. By introducing an evolution equation for the endurance function, the final collapse can be assumed to occur when the damage D is complete, that is when D reaches the unity. The parameters of this model, which adopts the stress invariants and the deviatoric stress invariants to quantify the damage phenomenon, are determined through a Genetic Algorithm once experimental data on the fatigue behaviour of the material being examined are known for some complex stress histories. With respect to traditional approaches to multiaxial fatigue assessment, the proposed model presents the following advantages: (1) the evaluation of a critical plane is not necessary; (2) no cycle counting algorithm to determine the fatigue life is required, because it considers the progressive damage process during the fatigue load history; (3) the model can be applied to any kind of stress history (uniaxial cyclic loading, multiaxial in‐phase or out‐of‐phase cyclic loading, uniaxial or multiaxial random loading).

A notch multiaxial-fatigue approach based on damage mechanics

The fatigue assessment of structural components under complex multiaxial stresses (cyclic or random stress histories) can be conveniently tackled by means of damage mechanics concepts. In the present paper, a model for notch fatigue damage evaluation in the case of an arbitrary multiaxial loading history is proposed by using an endurance function which quantifies the damage accumulation in the material up to the final failure. The material collapse can be assumed to occur when the damage is complete, that is, when the parameter D reaches the unity. In the case of notched structural components, such a damage parameter D must be evaluated by taking into account the stress value as well as the gradient effect at the notch root. The proposed model, which also employs the stress invariants and the deviatoric stress invariants to quantify the damage phenomenon, is calibrated through a Genetic Algorithm once experimental data on the fatigue behaviour of the material being examined are known for some uniaxial or complex stress histories. The model presents the advantages to be mechanically based and to not require any evaluation of a critical plane and any loading cycle counting algorithm to determine the fatigue life.

Hysteresis in kinking nonlinear elastic solids and the Preisach-Mayergoyz model

Herein we show that the stress-induced, dislocation-based, elastic hysteric loops of kinking nonlinear elastic solids---polycrystalline cobalt, $10\text{ }\text{vol}\text{ }\mathrm{%}$ porous ${\text{Ti}}_{2}\text{AlC}$, and fully dense ${\text{Ti}}_{3}{\text{SiC}}_{2}$---obey the scalar Preisach-Mayergoyz phenomenological model because they exhibit wiping out and congruency, two necessary and sufficient tenets of the model. We also demonstrate the power of the model in predicting the response of these materials to complex stress histories, as well as, determining the distributions of the threshold and friction stresses associated with the incipient kink bands---the fundamental microscopic units responsible for kinking nonlinear elasticity.

Preliminary observations on the impact of complex stress histories on sandstone response to salt weathering: laboratory simulations of process combinations

Historic sandstone structures carry an inheritance, or a ‘memory’, of past stresses that the stone has undergone since its placement in a facade. This inheritance, which conditions present day performance, may be made up of long-term exposure to a combination of low magnitude background environmental factors (for example, salt weathering, temperature and moisture cycling) and, superimposed upon these, less frequent but potentially high magnitude events or ‘exceptional’ factors (for example, lime rendering, severe frost events, fire). The impact of complex histories on the decay pathways of historic sandstone is not clearly understood, but this paper seeks to improve that understanding through the use of a laboratory ‘process combination’ study. Blocks of quartz sandstone (Peakmoor, from NW England) were divided into subsets that experienced different histories (lime rendering and removal, fire and freeze–thaw cycles in isolation and combination) that reflected the event timeline of a real medieval sandstone monument in NE Ireland, Bonamargy Friary (McCabe et al. 2006b). These subsets were then subject to salt weathering cycles using a 10% salt solution of NaCl and MgSO4 that represents the ‘every-day’ stress environment of, for example, sandstone structures in coastal, or polluted urban, location. Block response to salt weathering was monitored by collecting, drying and weighing the debris that was released as blocks were immersed in the salt solution at the beginning of each cycle. The results illustrate the complexity of the stone decay system, showing that seemingly small variations in stress history can produce divergent response to salt weathering cycles. Applied to real-world historic sandstone structures, this concept may help to explain the spatial and temporal variability of sandstone response to background environmental factors on a single facade, and encourage conservators to include the role of stress inheritance when selecting and implementing conservation strategies.

A comprehensive description for shape memory alloys with a two-phase mixture modelincorporating the conventional theory of plasticity

A comprehensive description for the constitutive behavior of polycrystalline shape memoryalloys (SMAs) is proposed based on a two-phase mixture model incorporating theconventional theory of plasticity. An SMA is composed of austenite and martensite phases,and its constitutive behavior should be the combination of the individual behavior of eachof the two phases. In the interested ranges of stress and temperature, the behavior of theaustenite is assumed to be linearly elastic while that of martensite is assumed tobe elastoplastic. The main features of SMAs, such as shape memory effect andpseudoelasticity, can be successfully replicated with the proposed constitutive model. Theconstitutive behavior of SMA Au–47.5 at.% Cd subjected to uniaxial forward and reverseloading and the pseudoelasticity of Cu–Al–Zn–Mn SMA polycrystal subjected toproportional and nonproportional complex stress or strain histories are simulated andcompared with the experimental results.

A comprehensive description for shape memory alloys with a two-phase constitutive model

A comprehensive description for the constitutive behavior of polycrystalline shape memory alloys (SMAs) is proposed based on the concept that a SMA is dynamically composed of austenite and martensite, the constitutive behavior of which is a dynamic combination of the individual behavior of each of the two phases. In the interested ranges of stress and temperature the behavior of austenite is assumed to be linearly elastic while that of martensite elastoplastic. The main features of SMAs such as ferroelasticity at lower temperature, shape memory effect (SME), pseudoelasticity at higher temperature and other typical features can be successfully replicated with the proposed constitutive model. The ferroelasticity, pseudoelasticity and SME of SMA Au–47.5 at.%Cd subjected to uniaxial forward and reverse loading and the pseudoelasticity of Cu–Al–Zn–Mn SMA polycrystal subjected to proportional and nonproportional complex stress or strain histories are analyzed and compared with the experimental results.

Prediction of Anomalous Hygrothermal Effects in Polymer Matrix Composites

Theory of irreversible thermodynamics is applied to derive governing equations for history-dependent diffusion in polymers and polymer matrix composites from first principles. A special form for Gibbs' free energy is introduced using stress, temperature, and moisture concentration as independent state variables. The resulting governing equations are capable of modeling the effect of interactions between complex stress, temperature, and moisture histories on the diffusion process within an orthotropic material. Since the mathematically complex nature of the governing equations precludes a closedform solution, a variational formulation is used to derive the weak form of the nonlinear governing equations which are then solved using the finite element method. For model validation, the model predictions are compared with published data for the special case of isothermal diffusion in an unstressed graphite/epoxy symmetric angle-ply laminate.

Modeling of Anomalous Moisture Diffusion in Polymer Composites: A Finite Element Approach

Theory of irreversible thermodynamics is applied to derive governing equations for history-dependent diffusion in polymers and polymer matrix composites from first principles. A special form for Gibb's free energy is introduced using stress, temperature, and moisture concentration as independent state variables. The resulting governing equations are capable of modeling the effect of interactions between complex stress, temperature, and moisture histories on the diffusion process within an orthotropic material. Since the mathematically complex nature of the governing equations precludes a closed-form solution, a variational formulation is used to derive the weak form of the nonlinear governing equations which are then solved using the finite element method. For model validation, the model predictions are compared with published experimental data for the special case of isothermal diffusion in an unstressed graphite/epoxy symmetric angle-ply laminate.

Separation of multiple stress events by fault striation analysis: an example from Variscan and younger structures at Ogmore, South Wales

The study of minor structures in Carboniferous and Triassic sedimentary rocks at Ogmore- by-Sea, Bridgend. reveals that the observed microstructures are the consequence of successive brittle deformation events. Age relationships can be deduced from sets of structures consisting of conjugate faults, oblique slip faults, tension gashes and stylolites. from which deductions can be made about the orientations of principal stresses corresponding to pre-and post-Triassic events. The demonstrable polyphase tectonic history at Ogmore and the occurrence of large numbers of striated faults at four sites allow the opportunity of testing a newly proposed strategy for palaeostress analysis from striated faults with complex stress histories. The new technique, based on the statistical procedure of cluster analysis, involves the sorting of fault-slip data into coherent dynamic setsasa preliminary stage of formal stress inversion. The fault sets separated using this technique yield stresses which are similar to those deduced from field observations. Four stress configurations are distinguished, of which two are pre-Triassic in age. Correlations with previously derived stresses are discussed.

Laboratory Evaluation of Horizontal Stress in Overconsolidated Sands

Abstract This paper describes a method for the determination of in situ horizontal stresses of heavily overconsolidated sands using a stress-path triaxial apparatus. This method was proposed by Garga and Khan (1991), who applied it to overconsolidated clays. The proposed method is based on the concept that if the radial stress exceeds the in situ horizontal stress while maintaining the axial stress constant and equal to the in situ vertical effective stress, only then will the specimen experience significant axial strain. In this investigation, the above method was applied to specimens of known stress histories of overconsolidated sand. Simulation of complex stress histories was carried out by subjecting the soil specimens to one and two cycles of loading in drained conditions (rate of loading or unloading: 0.05 kPa/min). It was found that the proposed method replicated the simulated in situ horizontal stress exactly. The technique is capable of estimating K0 irrespective of the previously imposed stress history.

New Solutions describing the formation of interparticle necks in solid-state sintering

The formation of a neck between spherical particles by surface and grain boundary diffusion is modelled by three independent methods. First, an accurate numerical solution is provided. Second, closed-form similarity solutions are derived, which are exact for short times in the limiting cases of small and large δDs/δDb ratios. Third, approximate analytical solutions are developed based on a thermodynamic variational principle. The latter method is probably the most versatile on e, since its results are formulated as coupled evolution equations for the neck size and the center-to-center approach of the spheres. As such they are well suited to deal with variable stress and temperature histories as encountered by the material during inhomogeneous sintering. Where the similarity solutions are valid (zero stress, short times, small or large δDs/δDb), they confirm the results of the approximate method. Compared to the fully numerical method the approximate method usually works well, also for complex stress histories, but has its limitations when the stress becomes tensile and the neck shrinks rapidly in a crack-like mode.

New solutions describing the formation of interparticle necks in solid-state sintering

The formation of a neck between spherical particles by surface and grain boundary diffusion is modelled by three independent methods. First, an accurate numerical solution is provided. Second, closed-form similarity solutions are derived, which are exact for short times in the limiting cases of small and large δD s/ δD b ratios. Third, approximate analytical solutions are developed based on a thermodynamic variational principle. The latter method is probably the most versatile on e, since its results are formulated as coupled evolution equations for the neck size and the center-to-center approach of the spheres. As such they are well suited to deal with variable stress and temperature histories as encountered by the material during inhomogeneous sintering. Where the similarity solutions are valid (zero stress, short times, small or large δD s/ δD b), they confirm the results of the approximate method. Compared to the fully numerical method the approximate method usually works well, also for complex stress histories, but has its limitations when the stress becomes tensile and the neck shrinks rapidly in a crack-like mode.

Mathematical background for applying multiple axes random stress histories in the fatigue testing of offshore tubular joints

Fatigue testing of large scale tubular joints has progressed to the point where a realistic in-service stress history can be used to obtain more representative fatigue data. In order to establish some standard histories to correlate data colleted by different laboratories and to characterize the in-service load histories for fixed offshore structures in the North Sea, an international committee on Wave Action Standardized History (WASH) was set up. After several years of collaboration, the first set of WASH recommendations has been finalized. These recommendations include the establishment of a standard stress-time history generation framework and three sets of input data for different configurations in the North Sea. While the WASH development is being continued for more complex stress histories, enhancement of the first standard framework has also been undertaken for application in multiple axes fatigue testing of tubular joints. This paper outlines the standard WASH generator and reports the enhancement required for generating and applying multiple axes of stress histories to fatigue testing. The spatial arrangement and mechanical interaction of the multiple actuators will be discussed and analysed. Sample histories are used to demonstrate the applications in tubular T joints.

On modelling steady state and transient creep of polycrystalline solids

A constitutive model is proposed to describe creep deformation of polycrystalline materials under complex stress and temperature histories. The concept of piecewise linear effective stress—creep strain rate relationship is utilized. A key assumption in this model is that the back stress under a given stress and temperature reaches a saturation point. This saturation point corresponds to the steady state condition.

A CONSTITUTIVE EQUATION OF SAND AS ANISOTROPIC ELASTO-PLASTIC BODY

A sand is a complicated material that is associated with dilatancy by loading and is also largely influenced by stress histories. In order to represent the characteristics of sand, subsequent anisotropy, which is induced by dilatancy accompanying plastic deformation, is evaluated on the basis of the results obtained from simple laboratory tests under axisymmetric stress conditions. Furthermore, an elasto-plastic stress-strain relation for sand is derived from considering a sand as a strain hardening material not only for shear but also for compression and adopting stress-dilatancy relation. From comparisons of the calculated results with the strains measured in the stress path tests with complex stress histories, it is shown that the proposed equation may be useful in prediction of the stress-strain behaviour of sands.

Creep of 2618 Aluminum Under Side-Steps of Tension and Torsion and Stress Reversal Predicted by a Viscous-Viscoelastic Model

Combined tension and torsion creep experiments are reported in which (A) one stress component was increased or decreased while the other remained constant; (B) one stress component was removed while the other remained constant; (C) torsion was partially or fully reversed with or without simultaneous constant tension. Among the observed features of the experimental results were the following: when one stress component was removed the creep from the other component was unaffected; upon small reductions in stress there was no recovery-type behavior; and when torsion was fully reversed, all prior strain was wiped out. A nonlinear viscous-viscoelastic model was used for which the material constants were derived from constant-stress creep and recovery data and previously reported. This model, together with certain necessary modifications, was used to compute the creep resulting from the complex stress histories described. Most features of the experimental results were predicted reasonably well by the modified theory.