Cyclic Plastic Behavior Research Articles

Low Cycle Fatigue and Cyclic Plasticity Behavior of Indian PHWR/AHWR Primary Piping Material

Abstract The integrity assessment of the primary piping components needs to be demonstrated under normal operation cyclic loadings as well as under complex cyclic loadings of extreme magnitude as may come during a severe earthquake event. In order to understand material's cyclic plasticity and fatigue-ratcheting behaviour, systematic experimental and analytical investigations have been carried out on specimens of SA333Gr.6 carbon steel and SS304LN stainless steel. The material specification of SA333Gr.6 is same as used in Primary Heat Transport (PHT) piping of Pressurized Heavy Water Reactors (PHWRs) and material specification of SS304LN steel is same as proposed for Indian Advance Heavy Water Reactor's (AHWR's) Main Heat Transport (MHT) piping. The test program included the tensile, axial fatigue and uniaxial ratcheting tests to establish the material's mechanical properties and cyclic plasticity behavior. The results of these tests have been investigated in details using few popular finite element cyclic plasticity models to understand and quantify the material's cyclic plasticity behavior. The studies revealed the need to modify the Chaboche model to simulate the LCF/cyclic plasticity and ratcheting under different strain/stress amplitudes loading conditions. On accounting for modification, the Chaboche model nicely predicted the LCF and ratcheting response for all the tests. The tests, finite element analyses result and their interpretations have been presented in this paper.

Parameter-refreshed Chaboche model for mild steel cyclic plasticity behaviour

The development of a steel material model in order to follow the cyclic plastic behaviour is essential in seismic design. The authors present an improved Chaboche model for the cyclic mechanical behaviour of structural steel. The model is based on the combination of nonlinear kinematic and multi-linear isotropic hardening with a parameter refreshing method. This model can consider the different physical phenomena of steel bahviour under cyclic loading. The developed model is verified by experimental results; the calculation of model parameters, the effect of the applied constants and the calibration are discussed.

Modeling and Finite Element Simulation of Low Cycle Fatigue Behaviour of 316 SS

Abstract In this model the cyclic plastic behaviour in the transition cycle (from virgin state to saturated state) has been studied for the material SS316. The dynamic recovery terms in Chaboche's kinematic hardening law have been modified with a memory function to include cyclic hardening/softening behaviour during transition cycles. The memory function has been calibrated for this material to obtain a saturated value at the stable hysteresis loop. The hardening rate (increase in hardening stress per cycle) is also matched by proper calibration constant. All the material constants have been derived from uniaxial strain controlled low cycle fatigue (LCF) test results from virgin state to saturated state at stable hysteresis loop. The material model developed with the kinematic hardening rules has been plugged into a Finite Element (FE) program. The results obtained from FE simulations have been compared with the experimental results at different strain amplitudes.

A numerical approach for predicting shakedown limit in ratcheting behavior of materials

Studying the ratcheting and shakedown behavior of materials under cyclic loading is significant for controlling structural deformation and improving the service lifetime of materials. In this study, cyclic loading tests were performed on DH36 steel at room temperature under various conditions while evaluating the effects of the loading waveform, the loading rate and the stress ratio to reveal the material characteristics of ratcheting and shakedown behavior and to provide an experimental basis for proposing and implementing a numerical method that predicts the shakedown limit in this type of cyclic plastic behavior. A numerical analysis method using the plastic deformation energy as a shakedown criterion was proposed based on the energy dissipation phenomena observed in the tests. The method was then applied to two classic examples of shakedown analysis by computation and was compared with related results from the literature to evaluate its effectiveness and reliability. This method provides a new approach for the numerical analysis of the material shakedown limit.

High Cycle Fatigue and Cyclic Plastic Deformation Behaviour of High Temperature Oxidation Resistant Titanium Aluminide Coated IMI 834 Alloy at 873 K

High cycle and force-controlled (HCF) as well as low cycle fatigue (LCF) behaviour of titanium alloy IMI 834 was comparatively studied in bare condition and with titani-umaluminide (Al2Ti) coating, at 873K in air, for compressor disc of aero engines. HCF testing of bare and Al2Ti coated IMI 834 alloy at 873 K in air revealed t hat the coated materials has higher lifetime than the bare alloy.However, for low cycle, high stress lifetimes, the unprotected bare alloy is stronger, possibly due to early crack formation and growth in coated layer. In the case of LCF tests at higher values of total strain amplitudes Al2Ti coated IMI 834 alloy has longer fatigue life (Nf ) as compared to the bare IMI 834 alloy which appears to be due to load shift-ing to the coat, but at lower values of total strain amplitude, Al2Ti coating on IMI 834 alloy seems to have no effect on Nf . Higher values of cyclic strength coeffici-ent (K0) and cyclic hardening exponent (n0) for coated IMI 834 alloy indicate that coating offers resistance to cyclic plastic deformation at 873 K in air, and hence is beneficial. The coating adheres well to the substrate and is also fairly resistant to high temperature corrosion in sea water atmosphere at 873 K.

Modeling of uniaxial ratchetting behavior of SA333 carbon manganese steel

The paper deals with uniaxial ratcheting phenomenon of cyclic plasticity behavior of the materials SA333 carbon Manganese steel. A mechanistic model for the ratcheting phenomenon has been proposed. It is observed that von Mises yield criterion together with Chaboche’s kinematic hardening rules are not sufficient to model ratcheting phenomenon. Other associated phenomena like plastic strain memory surface, back stress memory points and over all the extra hardening behavior have to be incorporated to get a complete material model for ratcheting. The proposed model assembled all these ideas together with von Mises yield criterion and Chabache’s kinematic hardening rule. Low cycle fatigue tests and uniaxial ratcheting tests have been conducted for the materials. The material constants are identified and derived from experimental results. The ratcheting coefficients have been properly calibrated with these material constants. The material model, as mentioned above, for the ratcheting phenomenon has been implemented in an elastic plastic finite element code. The ratcheting results for different stress controlled ratcheting loads have been computed. The good feature of this model is that it reduces to symmetric low cycle fatigue model when loop closes.

Description of Planer Anisotropy and Cyclic Plasticity Behavior of Aluminum Sheet Based on Crystal Plasticity Theory

In sheet metal forming, the anisotropy and the Bauschinger effect of sheets affect greatly their formability. This paper discusses how the planar anisotropy and cyclic plastic behavior (the Bauschnger effect and cyclic workhardening characteristics) correlate with the crystallographic texture based on the crystal plasticity analysis on A5052-O sheet. The analytical predictions of r-values and the cyclic stress-strain responses are compared with the experimental observations (S. Tamura et al., Materials Trans, 52-5 (2011), pp.868-875).

Warpage variations of Si/solder/OFHC-Cu layered plates subjected to cyclic thermal loading

Warpage variations of Si/solder/OFHC-Cu layered plates under cyclic thermal loading were investigated as a fundamental subject for inverter power modules. Two different solders, fully annealed and as-received OFHC-Cu plates, and three thickness ratios of the Si and Cu layers were used for the layered plates tested. It was experimentally observed that the initial warpage induced by soldering either grew or recovered with an increase in the number of temperature cycles: the cyclic growth of warpage occurred when the OFHC-Cu layer was fully annealed before soldering and was relatively thick. By performing 3D finite element analysis using available material data, it was then shown that the observed cyclic growth/recovery of warpage can be simulated well if an appropriate constitutive model is employed for the cyclic plastic behavior of OFHC-Cu plates.

On the efficiency of algorithms for computing a micromechanical constitutive equations coupled with damage

The numerical solution of non-linear constitutive relations problems represents an important topic since it needs relatively an important computational time, especially for micromechanical approaches arising in rate-dependent non-associated elasto-inelasticity coupled with damage. Thus, a recent developed micromechanical model with damage induced anisotropy concept is used [1] to study numerically its responses under different cyclic loading paths.Hence, the main goal of this study is based on the formulation and the numerical integration of the model describing the cyclic plasticity behavior. Three well-known algorithms are used comparing their computing times and precisions for different cyclic loadings. These are the algorithms of Runge–Kutta of 2nd and 5th orders with an adaptive step (noted respectively by RK2 and RK5). The algorithm of Burlisch–Stöer (MDP) is also presented and applied. According to the obtained results, it appears that the algorithm MDP gives the best compromise between the computational time and its precision with respect to the used algorithms for such a model especially in the case where the damage is coupled with elasto-inelastic behavior.

Cyclic behaviour and plastic strain memory effect of 55NiCrMoV7 steel under low cycle fatigue

Cyclic plastic behaviour of tempered martensitic tool steel 55NiCrMoV7 with four different initial hardness levels was studied under tensile-compress low cycle fatigue (LCF) in the temperature range from room temperature up to 873 K. Cyclic behavior tests and strain memory effect tests were performed in symmetrical tensile-compression strain loading with a triangular waveform. The results show that steel represents cyclic softening behaviour. The cyclic stress response generally shows an initial exponential softening for the first few cycles, followed by a gradual softening without saturation. Cyclic stress response depends on strain rate. The steel represents cyclic viscoplasticity. The steel shows the plastic strain memory effects at each test temperature, the cyclic stress and cumulated plastic strain depends on the history of cyclic loading. If strain amplitude increases after a previous linear softening is achieved, a new rapid non-linear cyclic softening appears. In the opposite, if strain amplitude decreases from higher one to lower, softening remains linear, and moreover σ-p curve goes along the previous way at the previous same strain loading level. It was discussed that the influences of initial hardness, fatigue temperature, strain rate and cyclic strain amplitude on cyclic plasticity of the steel.

1617 オーステナイト系ステンレス鋼の大ひずみ繰返し変形挙動とそのモデル化(機械材料・材料加工VI)

1617 オーステナイト系ステンレス鋼の大ひずみ繰返し変形挙動とそのモデル化(機械材料・材料加工VI)

Cyclic plastic behavior analysis based on the micromorphic mixed hardening plasticity model

In this paper, a small strain micromorphic elasto-plastic model with isotropic/kinematic hardening is presented for modeling the size effect and Bauschinger effect in material with microstructure. A nonlinear kinematic hardening model is embedded into the micromorphic framework by employing a backstress, a micro-backstress and a micro-couple-backstress in a physical way. The material intrinsic length scale is introduced in the constitutive law, leading to the presence of higher order stress. The present model is further implemented into a 2D plane strain finite element frame with a fully implicit stress integration scheme. The generalized consistent tangent modulus is derived to achieve the parabolic convergence of the global nodal force equilibrium equation. Two numerical examples, including a thin film and a plate with underlying structures subjected to cyclic loading, are analyzed to verify the theoretical developments and numerical formulations. Plastic behaviors in micromorphic continuum, such as size effect, Bauschinger effect, ratcheting effect and plastic shakedown phenomenon, are investigated.

Experimental and numerical simulation of carbon manganese steel for cyclic plastic behaviour

The paper deals with finite element modeling of saturated low cycle fatigue and the cyclic hardening phenomena of the materials Sa333 grade 6 carbon steel and SS316 stainless steel. Von Mises’ yield function and Chaboche’s kinematic hardening rules have been used. The recall terms of Chaboche’s kinematic hardening rule is calibrated with a memory function. The evolution law of the memory function is determined from experimental observations. The material constants are identified and derived from experimental results. The FE simulated results are compared with the experimental results from virgin state to saturation state of the materials. Keywords: cyclic plasticity, kinematic hardening, low cyclic fatigue, dilatation

Cyclic plastic behaviour of primary heat transport piping materials: Influence of loading schemes on hysteresis loop

Cyclic plastic deformation behaviour of 304LN stainless steel and SA333 Gr.6 C–Mn steel has been investigated employing a constant, increasing and decreasing strain amplitude cycling. Influence of loading scheme on cyclic plasticity characterizing parameters such as cyclic hardening/softening and Masing behaviour are examined. Additional hardening is identified with change in loading scheme and the hardening/softening sustains a dependency of prior load history in both the materials. Masing behaviour is not a common phenomenon in many engineering materials and both the materials in this investigation exhibited a non-Masing behaviour, however, the degree of deviation from Masing varied with the loading scheme. Microscopic evidences to explain the non-Masing behaviour are presented. The experimental investigations show that change in yield stress alone could not be used to explain the hardening/softening behaviour. However, sufficient experimental support is gathered to show that the strain range effect (non-Masing behaviour) is due to change in yield stress and can be explained by a continuous distribution of yield levels.

True stress control asymmetric cyclic plastic behavior in SA333 C–Mn steel

Asymmetric cyclic loading in the plastic region can leads to progressive accumulation of permanent strain. True stress controlled uniaxial asymmetric cycling on SA333 steel is conducted at various combinations of mean stress and stress amplitude in laboratory environment. It is investigated that fatigue life increases in the presence of mean stress. Plastic strain amplitude and hysteresis loop area are found to decrease with increasing mean stress. A huge difference of life and ratcheting strain accumulation is found in engineering and true stress controlled tests.

Analysis of stress distribution in compression precracking

Purpose – The paper aims to shed some light on the effect of the notch/crack‐tip stresses and their role on the cyclic plasticity and crack growth behavior in compression‐compression fatigue.Design/methodology/approach – Compression precracking was studied using 2D finite element analysis for CT specimen. The final crack length and the shape of the crack front were compared with those obtained experimentally.Findings – It has been found that cyclic plasticity and stress redistribution govern the observed fatigue crack growth behavior in compression‐compression precracking. Only the internal stress corresponding to Pmax shows a significant redistribution with the crack extension whereas the stress corresponding Pmin is not affected by the increase of crack length.Research limitations/implications – This results are limited to Mode I cracking.Practical implications – It supports that two thresholds, ΔKth and Kmaxth, govern the fatigue crack behavior. When the contribution from the internal tensile stress is...

Electronic Speckle‐Pattern Interferometry Measurements of Structural Ratcheting Strain

Abstract: Several tensile specimens with a central hole were subjected to a cyclic loading for which the Von Mises stress was beyond the initial yield stress in the vicinity of the hole. The tensile machine was fixed together with a phase‐shifting electronic speckle‐pattern interferometry measurement bench that makes it possible to perform strain measurement along the tensile axis. The plastic strain map corresponding to the 30th cycle was obtained. For the considered measurement field, the resolution of the strain measurement is close to 10−5. By varying the loading, it was possible to detect and observe the deformation corresponding to an early stage of the ratcheting phenomenon. The non‐ratcheting cyclic plasticity behaviour was not observed during the 30th cycle. In the Discussion section, the experimental results were interpreted using Melans’s theorem, which allowed us to determine an upper bound for the yield stress. Eventually, it is shown that the procedure followed in this work could be a way to obtain some interesting data related to the material behaviour laws.

Low cycle lifetime assessment of Al2024 alloy

The 2024-T351 aluminum alloy is extensively used for fabricating aircraft parts. This alloy shows a relatively low ductility at room temperature and is generally heat treated in various conditions to suit particular applications. The present study experimentally and numerically analyzes the damage mechanism of an Al2024-T351 plate (short transverse direction) subjected to multi-axial stress states. The purpose of this work is to predict the cyclic lifetime of the considered alloy, based on the local approach of damage evolution using continuum damage modeling (CDM). The experimental program involves different kinds of specimens and loading conditions. Monotonic and cyclic tests have been conducted in order to measure the mechanical response and also to perform micromechanical characterization of damage and fracture processes. The cyclic plasticity behavior has been characterized by means of smooth cylindrical specimens. For analyzing the evolution of plastic deformation and damage under multi-axial stress conditions, cyclic loading tests in the low cycle regime have been conducted on different round notched bars. The predictions of the CDM were compared to the experimentally observed mechanical response and to the micromechanical characterization of damage. Emphasis was placed on the prediction of the number of cycles to failure.

A study on the interaction between fretting wear and cyclic plasticity for Ti–6Al–4V

The fretting wear behaviour of Ti–6Al–4V is experimentally investigated using a cylinder-on-flat specimen arrangement for different loads, strokes and numbers of fretting cycles, including partial slip and gross sliding conditions. An elastic–plastic, finite element (FE) based, incremental wear simulation approach is employed to study the evolution of the surface and sub-surface fretting variables, using a kinematic hardening (continuum) plasticity model to represent the cyclic plasticity behaviour. The predicted evolution of plastic deformation and fretting variables, such as contact pressure, relative slip, sub-surface stresses and critical-plane Smith–Watson–Topper (multiaxial) fatigue parameter, due to the simulated wear are compared with the observed wear scar characteristics and locations of crack initiation. It is shown that the characteristics of predicted plastic strain and damage accumulation are significantly different for the gross sliding and the partial slip cases and that the differences can be correlated with the observed differences in surface morphology and surface cracking. It is shown that the location of plasticity due to shear yielding at the surface promotes wear across the contact region for the gross sliding case and at the stick–slip interface for the partial slip case.

Crack initiation and growth path under multiaxial fatigue loading in structural steels

In real engineering components and structures many accidental failures occur due to unexpected or additional loadings, such as additional bending or torsion. There are many factors influencing the fatigue crack paths, such as the material type (microstructure), structural geometry and loading path. It is widely believed that fatigue crack nucleation and early crack growth are caused by cyclic plasticity. This paper studies the effects of multiaxial loading paths on the cyclic deformation behaviour, crack initiation and crack path. Three types of structural steels are studied: Ck45, medium carbon steel, 42CrMo4, low alloy steel and the AISI 303 stainless steel. Four biaxial loading paths were applied in the tests to observe the effects of multiaxial loading paths on the additional hardening, fatigue crack initiation and crack propagation orientation. Fractographic analyses of the plane orientations of crack initiation and propagation were carried out by optical microscope and SEM approaches. It is shown that these materials have different crack orientations under the same loading path, due to their different cyclic plasticity behaviour and different sensitivity to non-proportional loading. Theoretical predictions of the damage plane were conducted using the critical plane approaches, either based on stress analysis or strain analysis (Findley, Smith–Watson–Topper, Fatemi–Socie, Wang–Brown–Miller, etc). Comparisons of the predicted crack orientation based on the critical plane approaches with the experimental observations for the wide range of loading paths and the three structural materials are shown and discussed. Results show the applicability of the critical plane approaches to predict the fatigue life and crack initial orientation in structural steels.