Constitutive and damage modelling of H11 subjected to low‐cycle fatigue at high temperature

Hot‐work tool steel H11 is extensively applied in extrusion industries as extrusion tools. The understanding of its mechanical properties and damage evolution as well as failure is crucial for its implementation. In this paper, a finite element (FE) model employing Chaboche unified constitutive model and ductile damage rule is proposed to simulate the mechanical responses of H11 subjected to low‐cycle fatigue (LCF). Accumulated inelastic hysteresis energy is adopted to demonstrate the impact on damage initiation and evolution rules. A series of tension and LCF experiments were conducted to investigate H11's mechanical properties and its deterioration processes. In addition, to deeply understand the deformation and damage mechanism, scanning electron microscope (SEM) investigations were performed on the fracture section of gauge‐length part of the specimen after failure. Furthermore, the parameters in both constitutive model and damage rule are identified based on experimental data. The comparison of the hysteresis loop of the first cycle and stable cycle with different strain amplitudes demonstrates that the Chaboche constitutive model provides high precision to predict the evolution of mechanical properties. Based on the reliable achieved constitutive model, LCF behaviour prediction with damage rule was executed successfully using FE model and gains a good agreement with the experiments. It is believed that the proposed FE method lays the foundation of structure analysis and rapid design optimization in further applications.     

A continuum damage model applied to high-temperature fatigue lifetime prediction of a martensitic tool steel

High‐temperature operational conditions of hot work tool steels induce several thermomechanical loads. Depending on the processes, (i.e. forging, die casting or extrusion), stress, strain, strain rate and temperature levels applied on the material are nevertheless very different. Thus, lifetime prediction models need to be able to take into account a broad range of working conditions. In this paper, a non‐isothermal continuum damage model is identified for a widely used hot work tool steel AISI H11 (X38CrMoV5) with a nominal hardness of 47 HRc. This investigation is based on an extensive high‐temperature, low‐cycle fatigue database performed under strain rate controlled conditions with and without dwell times in the temperature range 300–600°C . As analysis of experimental results does not reveal significant time‐dependent damage mechanisms, only a fatigue damage component was activated in the model formulation. After normalization, all fatigue results are defined on a master Woehler curve defined by a nonlinear damage model, which allows the parameter identification. Last, a validation stage of the model is performed from thermomechanical fatigue tests.     

Influence of γ‐α′‐Phase Transformation in Metastable Austenitic Steels on the Mechanical Behavior During Tensile and Fatigue Loading at Ambient and Lower Temperatures

The present investigation is concerned with the three metastable austenitic steels AISI 304 (X5CrNi1810), 321 (X6CrNiTi1810), and 348 (X10CrNiNb189). In the temperature range ?60 °C ≤ T ≤ 25 °C tensile and fatigue tests were performed to characterize the mechanical and phase transformation behavior using stress‐elongation, stress–strain hysteresis, and magnetic measurements. The mechanical properties are significantly influenced by the temperature dependent deformation induced phase transformation from austenite to α′‐martensite which are combined with pronounced hardening processes. Furthermore microhardness measurements after fracture could be correlated with the results of the fatigue tests.     

A general framework for fatigue reliability analysis of a high temperature component

Fatigue reliability analysis for a high temperature component is a complex task due to the difficulties of doing experiments and uncertainties occurring in practical engineering. Researchers usually focus on the fatigue life scatter of standard specimens since the life data are easily available from fatigue tests. An alternative method is proposed in this paper which can replace the real tests of high temperature components with finite element (FE) simulation. A constitutive model coupled damage rule is utilized in this work to describe the cyclic stress‐strain response. Then, the FE simulations is incorporated into the general framework for reliability assessment. An adaptive least squares support vector machines with Latin hypercube sampling and learning function is employed to construct limit state function. To verify the accuracy and robustness of proposed method, a numerical example is utilized. In the end of this paper, a three‐layer structure extrusion container is applied for whole flowchart of fatigue reliability analysis.     

A new energy‐based method to evaluate low‐cycle fatigue damage of AISI H11 at elevated temperature

AISI H11 (X38CrMoV5‐1) hot‐work tool steel is widely used for making extrusion tools because of its good mechanical properties at high temperature and moderate cost. To predict its lifetime, an energy conservation‐based model was proposed in this paper by introducing the damage rate, which is expressed as the product of damage force and plastic strain rate. The strain‐controlled low‐cycle fatigue tests were conducted to obtain the parameters of the proposed model, while the stress‐controlled low‐cycle fatigue tests were used to validate the proposed model. The results demonstrate that the proposed model is accurate and reliable. Furthermore, the local misorientation was investigated by electron backscatter diffraction to analyse the correlation between the microstructure evolution and the cyclic behaviour, and crack propagation behaviour was identified.     

Life prediction of stainless steels by cyclic and stable hysteresis curves

Abstract

This study develops an analytical expression to describe the cyclic stress‐strain curve obtained from a series of fully‐reversed fatigue tests. A set of stress‐strain relationships is proposed to simulate the tensile branch of the stable hysteresis loop. The complete shape of the stable hysteresis loop is then constructed and the associated theoretical plastic work calculated by integrating the area within the enclosed curve. The theoretical plastic work is employed to predict the fatigue lives of the investigated materials on the basis of their respective stable plastic work per cyclelife curves. In this paper, the current mathematical derivations are based upon the endochronic theory of plasticity. The accuracy of the proposed set of stress‐strain relationships is verified by conducting fully‐reversed constant strain amplitude fatigue tests on AISI 316 and AISI 304 stainless steels. The experimental and simulation results are found to be in good agreement, hence confirming the accuracy of the proposed analytical stress‐strain relationships. Again, comparing the obverted and predicted fatigue lives, a good agreement is found between the two sets of results.     

HIGH TEMPERATURE FATIGUE DAMAGE IN THREE AUSTENITIC ALLOYS

Abstract— A series of cyclic strain controlled tests have been carried out at 600°C on three high temperature austenitic iron-based alloys. These alloys were AISI type 316 stainless steel, Alloy 800 H and Sandvik 253 MA. The tests were carried out under constant total strain control using a constant strain rate of 0.005 s⁻'. Damage mechanics was applied to the results in order to follow the accumulation of damage. By consideiing the changes in modulus throughout the life of each specimen it was found that damage evolution could be successfully predicted as a function of plastic strain range despite the fact that each alloy had been chosen because of a different stress response at 600°C, namely cyclic saturation, hardening, and softening followed by hardening for the AISI 316, 253 MA and Alloy 800 H respectively. Although each alloy accumulated fatigue damage in a similar manner the longer lives of Sandvik 253 MA and Alloy 800 H at a given total strain range were due to a smaller plastic strain component and a reduced stage I crack propagation rate. In the 253 MA alloy. slip was predominantly planar with some cells occasionally forming at high strain ranges. Slip was localized in Alloy 800 H due to the shearing of small γ precipitates. In the AISI 316 stainless steel, dislocation cells formed at all strain ranges. It is concluded that all these alloys accumulate damage similarly, independent of their deformation behaviour.     

The role of grain size in static and cyclic deformation behaviour of a laser reversion annealed metastable austenitic steel

Different grain sizes were created in a metastable 17Cr‐7Mn‐7Ni steel by martensite‐to‐austenite reversion at different temperatures using a laser beam. Two fully reverted material states obtained at 990°C and 780°C exhibited average grain sizes of 7.7 and 2.7 μm, respectively. The third microstructure (610°C) consisted of grains at different stages of recrystallization and deformed austenite. A hot‐pressed, coarse‐grained counterpart was studied for reference. The yield and tensile strengths increased with refined grain size, maintaining reasonable elongation except for the heterogeneous microstructure. Total strain‐controlled fatigue tests revealed increasing initial stress amplitudes but decreasing cyclic hardening and fatigue‐induced α′‐martensite formation with decreasing grain size. Fatigue life was slightly improved for the 2.7‐μm grain size. Contrary, the heterogeneous microstructure yielded an inferior lifetime, especially at high strain amplitudes. Examinations of the cyclically deformed microstructure showed that the characteristic deformation band structure was less pronounced in refined grains.     

Multiaxial creep–fatigue under anisothermal conditions

Because creep–fatigue is mainly studied in uniaxial tension, it is shown here how to proceed to perform both experiments and calculations under multiaxial loading and when the temperature varies both in time and space. The constitutive equations used are those of elasto‐visco‐plasticity coupled or not, to damage, with isotropic and kinematic hardening. It is shown that the unified damage law first proposed for ductile failure and then for fatigue may also be applied to multiaxial creep–fatigue interactions with a new expression for the damage threshold. The procedure for the identification of material parameters is described in detail. Finally, it is shown that the uncoupled calculation procedure, where damage is calculated as a post‐processing of an elasto‐visco‐plastic computation, gives satisfactory results in comparison to the fully coupled analysis; the latter being more accurate but very expensive in computer time.     

Constitutive modeling of creep-fatigue interaction for normal strength concrete under compression

Conventional approaches to model fatigue failure are based on a characterization of the lifetime as a function of the loading amplitude. The Wöhler diagram in combination with a linear damage accumulation assumption predicts the lifetime for different loading regimes. Using this phenomenological approach, the evolution of damage and inelastic strains and a redistribution of stresses cannot be modeled. The gradual degration of the material is assumed to not alter the stress state. Using the Palmgren–Miner rule for damage accumulation, order effects resulting from the non-linear response are generally neglected.In this work, a constitutive model for concrete using continuum damage mechanics is developed. The model includes rate-dependent effects and realistically reproduces gradual performance degradation of normal strength concrete under compressive static, creep and cyclic loading in a unified framework. The damage evolution is driven by inelastic deformations and captures strain rate effects observed experimentally. Implementation details are discussed. Finally, the model is validated by comparing simulation and experimental data for creep, fatigue and triaxial compression.     

The choice of cyclic plasticity models in fatigue life assessment of 304 and 1045 steel alloys based on the critical plane-energy fatigue damage approach

The present study intends to examine various cyclic plasticity models in fatigue assessment of 304 and 1045 steels based on the critical plane-energy damage approach developed earlier. Cyclic plasticity models of linear hardening, nonlinear, multi-surface, and two-surface were chosen to study fatigue damage and life of materials under proportional and non-proportional loading conditions. The effect of additional hardening induced due to non-proportional loading in 1045 steel and particularly in 304 steel was further evaluated as different constitutive models were employed. In the present study, the plasticity models were calibrated by the equivalent cyclic stress–strain curves. The merits of the models were then investigated to assess materials deformation under proportional and non-proportional loading conditions. Under non-proportional loading, the cyclic plasticity models were found to be highly dependent upon the employed hardening rule as well as the materials properties/coefficients.The stress and strain components calculated through constitutive laws were then used as input parameters to evaluate fatigue damage and assess the fatigue life of materials based on the critical plane-energy approach.The calculated values of stress components based on constitutive laws resulted in a good agreement with those of experimentally obtained under various loading paths of proportional and non-proportional conditions in 1045 steels. In 304 steel, the calculated stress components were however found in good agreement when plasticity models were employed for proportional loading conditions. Under non-proportional loading, the application of the multi-surface plasticity model in conjunction with the fatigue damage approach resulted in more reasonable results as compared with other plasticity models. This can be attributed to the motion of the yield surface in deviatoric stress space in the multi-surface model encountering additional hardening effect through estimated higher stress values under non-proportional loading conditions.Predicted fatigue lives based on the critical plane-energy damage approach showed such range of agreements as ±1.05–±3.0 factors in 1045 and 304 steels as compared with experimental life data when various constitutive plasticity models were employed.     

Simulations of stress distributions in crankshaft sections under fillet rolling and bending fatigue tests

The residual stresses due to fillet rolling and the bending stresses near the fillets of crankshaft sections under bending fatigue tests are important driving forces to determine the bending fatigue limits of crankshafts. In this paper, the residual stresses and the bending stresses near the fillet of a crankshaft section under fillet rolling and subsequent bending fatigue tests are investigated by a two-dimensional plane strain finite element analysis based on the anisotropic hardening rule of Choi and Pan [Choi KS, Pan J. A generalized anisotropic hardening rule based on the Mroz multi-yield-surface model for pressure insensitive and sensitive materials (in preparation)]. The evolution equation for the active yield surface during the unloading/reloading process is first presented based on the anisotropic hardening rule of Choi and Pan (in preparation) and the Mises yield function. The tangent modulus procedure of Peirce et al. [Peirce D, Shih CF, Needleman A. A tangent modulus method for rate dependent solids. Comput Struct 1984;18:875–87] for rate-sensitive materials is adopted to derive the constitutive relation. A user material subroutine based on the anisotropic hardening rule and the constitutive relation was written and implemented into ABAQUS. Computations were first conducted for a simple plane strain finite element model under uniaxial monotonic and cyclic loading conditions based on the anisotropic hardening rule, the isotropic and nonlinear kinematic hardening rules of ABAQUS. The results indicate that the plastic response of the material follows the intended input stress–strain data for the anisotropic hardening rule whereas the plastic response depends upon the input strain ranges of the stress–strain data for the nonlinear kinematic hardening rule. Then, a two-dimensional plane-strain finite element analysis of a crankshaft section under fillet rolling and subsequent bending was conducted based on the anisotropic hardening rule of Choi and Pan (in preparation) and the nonlinear kinematic hardening rule of ABAQUS. In general, the trends of the stress distributions based on the two hardening rules are quite similar after the release of roller and under bending. However, the compressive hoop stress based on the anisotropic hardening rule is larger than that based on the nonlinear kinematic hardening rule within the depth of 2 mm from the fillet surface under bending with consideration of the residual stresses of fillet rolling. The critical locations for fatigue crack initiation according to the stress distributions based on the anisotropic hardening rule appear to agree with the experimental observations in bending fatigue tests of crankshaft sections.     

Analysis of Fatigue Damage under Block Loading in a Low Carbon Steel

Abstract: The fatigue damage accumulation behaviour of the P355NL1 steel is characterised using block loading fatigue tests. First, the constant amplitude low‐cycle fatigue behaviour of the P355NL1 steel is evaluated through strain‐controlled fatigue tests of smooth specimens. Both fatigue and cyclic elastoplastic behaviours are analysed. Then, block loading is applied to identify the key features of the fatigue damage accumulation phenomena for the P355NL1 steel. The block loading is composed of two distinct low‐cycle constant amplitude strain‐controlled blocks. The first block is applied for a predefined number of loading cycles, being followed by a second block which is applied until failure. The block loading illustrates that fatigue damage evolves nonlinearly with the number of load cycles as a function of the strain amplitude. These observations suggest a nonlinear damage accumulation rule with load sequence effects. The linear Palmgren–Miner's rule used extensively in design is not verified for the P355NL1 steel. Finally, using the generated experimental data, the cyclic elastoplastic behaviour of the P355NL1 steel is modelled using a continuum plasticity model with nonlinear kinematic hardening, available in the commercial finite element code ansys ®.     

Material behaviour of a dual hardening steel under thermomechanical loading

Dual hardening steels are a group of metals, which reach their material properties through a combination of strengthening via carbides and intermetallic precipitates. Because of their combination of mechanical properties, dual hardening steels are a promising alloying concept for hot‐work applications. The applied materials for hot‐work applications have to meet certain requirements, such as high hardness, high thermal strength, thermal stability, and fracture toughness. In this paper, a dual hardening steel in different heat treatment conditions was tested under out‐of‐phase thermomechanical loading conditions. All tests were done under full reverse strain control and the minimum temperature was kept constant. In the thermomechanical fatigue tests, solution annealed samples reached higher lifetimes compared with aged specimens. The hardness measurements show that the starting procedure of the thermomechanical fatigue leads to an increase of the hardness approximate to the values of the specimens with the ageing heat treatment. Cyclic softening can be observed in the test with the highest maximum temperature of 600°C. An increase of the maximum temperature also causes a decrease of the lifetime.     

A constitutive equation for hot deformation range of 304 stainless steel considering grain sizes

A general constitutive equation based on the framework of invariant theory by consideration of hot deformation key variables and also the properties of the material such as initial grain size is presented in the current work. Soundness of the considered parameters to be used in the developed formula was initially verified based on the important axioms such as objectivity, entropy principle, and thermodynamics stability. To access the prediction ability of the method, the formula was simplified for the simple hot compression test. To evaluate the simplified formula, single-hit hot compression tests were carried out at the temperature range of 900–1100 °C under true strain rate of 0.01–1 s⁻¹ on a AISI 304 stainless steel. The capability of proposed formula for reproducing the variation of flow stress with strain and the strain hardening rate with stress for the resultant flow stress data was examined. The good agreement between model predictions and actual results signified the applicability of this method as a general constitutive equation in hot deformation studies.     

Variable amplitude cyclic deformation and fatigue behaviour of stainless steel 304L including step,periodic, and random loadings

This paper discusses cyclic deformation and fatigue behaviours of stainless steel 304L and aluminium 7075‐T6 under variable amplitude loading using strain‐controlled as well as load‐controlled tests. Load sequence effects were investigated in step tests with high‐low and low‐high sequences. For stainless steel 304L, strong hardening induced by the first step of the H‐L sequence significantly affects the fatigue behaviour, depending on the test control mode used. For periodic overload tests of stainless steel 304L, hardening due to the overloads was progressive throughout life and more significant than in H‐L step tests. For aluminium 7075‐T6, no effect on deformation behaviour was observed due to periodic overloads. However, the direction of the overloads was found to affect fatigue life, as tensile overloads led to longer lives, while compressive overloads led to shorter lives. Deformation and fatigue behaviours under random loading were also studied for the two materials. To correlate a broad range of fatigue life data for a material with strong deformation history effect, such as stainless steel, it is shown that a damage parameter with both stress and strain is required. The Smith‐Watson‐Topper parameter as such a parameter is shown to correlate the data reasonably well under different control modes and loading conditions.     

An energy‐based damage parameter for the life prediction of AISI 304 stainless steel subjected to mean strain

Abstract

This study extends the plastic strain energy approach to predict the fatigue life of AISI 304 stainless steel. A modified energy parameter based on the stable plastic strain energy density under tension conditions is proposed to account for the mean strain and stress effects in a low cycle fatigue regime. The fatigue life curve based on the proposed energy parameter can be obtained directly by modifying the parameters in the fatigue life curve based on the stable plastic strain energy pertaining to fully reversed cyclic loading. Hence, the proposed damage parameter provides a convenient means of evaluating fatigue life on the mean strain or stress effect. The modified energy parameter can also be used to explain the combined effect of alternating and mean strain/stress on the fatigue life. In this study, the mean strain effects on the fatigue life of AISI 304 stainless steel are examined by performing fatigue tests at different mean strain levels. The experimental results indicate that the combination of an alternating strain and a mean strain strongly influences the fatigue life. Meanwhile, it is found that the change in fatigue life is sensitive to changes in the proposed damage parameter under the condition of a constant strain amplitude at various mean strain levels. A good agreement is observed between the experimental fatigue life and the fatigue life predicted by the proposed damage parameter. The damage parameter proposed by Smith et al. (1970) is also employed to quantify the mean strain effect. The results indicate that this parameter also provides a reasonable estimate of the fatigue life of AISI 304 stainless steel. However, a simple statistical analysis confirms that the proposed damage parameter provides a better prediction of the fatigue life of AISI 304 stainless steel than the SWT parameter.     

THE INFLUENCE OF THE HARDENING STATE ON TIME DEPENDENT DAMAGE AND ITS CONSIDERATION IN A UNIFIED DAMAGE MODEL

Abstract— A model is presented for the prediction of the lifetime of metals in the high-temperature range under arbitrary variable multiaxial load. The definition of an internal variable for damage in continuum damage mechanics is adopted, which allows indirect measurement of damage via the deformation behaviour. To acquire some knowledge of damage evolution, damage is measured in two ways during uniaxial strain controlled cyclic tests: (a) a change of the modulus of elasticity and (b) a decrease of the peak stress. Surprisingly, both methods lead to results which are in good agreement. A new damage law is then developed (with reference to known models and lifetime rules) which is a modification of the creep damage law of Rabotnov that is extended by a dependence on the inelastic strain rate instead of the dependence on internal variables to take into account the hardening state. Uniaxial as well as multiaxial formulations of the new damage model (Inelastic Strain Rate Modified (ISRM) model) are presented.
The parameters of the ISRM model are determined with a view to applying them to AISI 316 L(N) austenitic steel. Some of the parameters are derived from standard creep experiments. To determine further parameters, the ISRM model is applied to uniaxial cyclic tests. Both failure behaviour and damage evolution are well described.