Plastic,viscoplastic and creep fracture problems with the boundary element method

The present paper shows the applicability of the dual boundary element method to analyse plastic, viscoplastic and creep behaviours in fracture mechanics problems. Several models with a crack, including a square plate, a holed plate and a notched plate, are analysed. Special attention is taken when the discretization of the domain is performed. In fact, for the plasticity and viscoplasticity cases, only the region susceptible to yielding was discretized, whereas the creep case required the discretization of the whole domain. The proposed formulation is presented as an alternative technique to study these kinds of nonlinear problems. Results from the present formulation are compared to those of the well‐established finite element technique, and they are in good agreement. Important fracture mechanic parameters like K_I, K_II, J‐integrals and C‐integrals are also included. In general, the results, for the plastic, viscoplastic and creep cases, exhibit that the highest stress concentrations are in the vicinity of the crack tip and they decrease as the distance from the crack tip is increased.     

考虑塑性徐变的高混凝土坝实测应变转换应力探讨

将应变计组实测应变转换为应力与混凝土的应力状态有关。针对高混凝土坝应力作用水平较高,当混凝土的应力超过一定的限度,混凝土将进入塑性徐变阶段,如果仍基于弹性徐变体的应力-应变关系进行实测应变的应力转换,获得的应力与实际情况不符。该文假设混凝土在高应力作用下将产生塑性流动,根据P.Perzyna假设计算黏塑性应变率,首先推导了最大拉应力屈服准则和Hsieh-Ting-Chen屈服准则的黏塑性应变率计算公式,接着推导了考虑塑性徐变的实测应变转换应力的计算公式,进而探讨了考虑塑性徐变的高混凝土坝实测应变转换为应力。实例分析表明:由于将实测应变转换为应力采用增量法进行计算,在转换过程中,某阶段的应力失真,必然导致后续转换应力的真实性,而考虑塑性徐变的实测应变转换的应力更符合实际情况。     

On the kinematics of finite-deformation plasticity

Summary A theory of finite deformation plasticity is developed which involves a multiplicative decomposition of the deformation gradient through the assumption that there exists a stress-free configuration which can be used to separate the elastic and plastic components of the response. By using the polar decomposition on the usual indeterminate elastic and plastic deformation tensors, two uniquely defined stress-free configurations can be identified. The structure of this theory is compared with that of a spatial theory involving the polar decomposition of the total deformation gradient. It is shown that for the special case of linear response between the stress and the elastic strain, the two theories are indistinguishable in terms of their stress responses.With 1 Figure     

In-plane and out-of-plane crack-tip constraint effects under biaxial nonlinear deformation

In-plane and out-of-plane constraint effects on crack-front stress fields under both elastic–plastic and creep conditions are studied by means of three-dimensional numerical analyses of finite thickness boundary layer models and plane strain reference solutions. This investigation is an extension of the plane strain solution obtained by Shlyannikov and Boychenko in 2008, with special attention on what constraint parameters existed in the nonlinear crack-tip fields in a finite thickness solid. Characterization of constraint effects is given by using the non-singular T-stress, the local triaxiality parameter, the factor of the stress-state in 3D cracked body and the second order term amplitude factor. The influence of nominal stress load biaxiality and creep time on the behavior of constraint factors is considered. Stresses and constraint factors from FEA at the crack-front on different planes in the thickness direction of the plate are compared with plane strain reference solutions. The results show that 3D-stress fields can be characterized in common with the local triaxiality parameter and factor of the stress-state in 3D solid by the three-term solution throughout the thickness even in the region near the free surface. It is found that there is a distinct relationship between the in-plane and the crack-front out-of-plane constraint factors which can be well captured using the relation between the second order term amplitude factor and remote boundary layer stress.     

On the Analysis of an EFG Method Under Large Deformations and Volumetric Locking

This work investigates a modified element-free Galerkin (MEFG) method when applied to large deformation processes. The proposed EFG method enables the direct imposition of the essential boundary conditions, as a result of the kronecker delta property of the special shape functions, constructed in the neighborhood of the essential boundary. The plasticity model assumes a multiplicative decomposition of the deformation gradient into an elastic and a plastic part and considers a J ₂ elasto-plastic constitutive relation that accounts for a nonlinear isotropic hardening. The constitutive model is written in terms of the rotated Kirchhoff stress and of the conjugate logarithmic strain measure. A total Lagrangian formulation is considered in order to improve the computational performance of the proposed algorithm. Here, aspects related to the volumetric locking are numerically investigated and an F-bar approach is considered. Some numerical results are presented, under axisymmetric and plane strain assumption, in order to attest the performance of the proposed method.     

Internal-variable constitutive model for rate-independent plasticity with hardening saturation surface

Summary An elastic-plastic material model with internal variables and thermodynamic potential, not admitting hardening states out of a saturation surface, is presented. The existence of such a saturation surface in the internal variables space — a consequence of the boundedness of the energy that can be stored in the material's internal micro-structure — encompasses, in case of general kinematic/isotropic hardening, a one-parameter family of envelope surfaces in the stress space, which in turn is enveloped by a limit surface. In contrast to a multi-surface model, noad hoc rules are required to avoid the intersection between the yield and bounding/envelope surface. The flow laws of the proposed model are studied in case of associative plasticity with the aid of the maximum intrinsic dissipation theorem. It is shown that the material behaves like a standard one as long as its hardening state either is not saturated, or undergoes a desaturation from a saturated hardening state, whereas, for saturated hardening states not followed by desaturation, it conforms to a combined yielding law in which the static internal variable rates obey a nonlinear hardening rule similar to that of analogous models of the literature. Additionally, the material is shown to behave as a perfectly plastic material for a class of (critical) saturated hardening states for which the stress state is on the limit surface. For nonassociative material models, it is shown that, under a special choice of the plastic and saturation potentials and through a suitable parameter identification, the well-known Chaboche model is reproduced. A few numerical examples are presented to illustrate the associative material response under monotonic and cyclic loadings.Dedicated to Prof. Dr. Dr. h. c. Franz Ziegler on the occasion of his 60th birthday     

Characterization of the nonlinear fracture resistance parameters for an aviation GTE turbine disc

The effects of crack growth rate model formulation, based on the elastic‐plastic and undamaged/damaged creep crack tip fields on the behaviour of low‐cycle fatigue and creep fracture resistance parameter behaviour, are represented by numerical calculations. The crack growth rate models include the fracture process zone size and damage parameters. An aviation gas turbine engine (GTE) rotating turbine disc is the focus of this innovative application of basic analytical and numerical solutions. For the GTE turbine disc, the constraint parameters, local fracture process zone sizes, and nonlinear plastic (K_p) and creep (K_cr) stress intensity factors are calculated by finite element analysis to characterize the fracture resistance along the semielliptical crack front as a function of the flaw aspect ratio, operation temperature, and disc rotation speed. Predictions of the creep‐fatigue crack growth rate and residual lifetime are given for different combinations of operation loading conditions and damage of the GTE turbine disc.     

Numerical study of the time dependent behavior of GN-10 structural ceramics in bend creep test

Numerical simulation coupled with a realistic material model for high temperature structural ceramics is used to gain insight into the time dependent behavior of ceramics under bending. No simplifications used in conventional analysis methods are invoked, such as the assumption of steady-state creep and omission of elastic deformation etc. As yet, the formulation is shown to be sufficiently general to adopt arbitrary material models. The final formulation results in a set of first order coupled ordinary differential equations that can be solved with ease by well-established numerical techniques. Due to the time-dependent and inhomogeneous stress and strain distributions in the specimen, it is generally difficult to extract intrinsic material information associated with a particular stress state from the bend creep test. The validity of the material parameters obtained from bend creep tests depends on the validity of the assumptions that underlie the analysis. More in situ measurements to obtain information besides deflection, such as the location of the neutral axis etc., will be helpful for interpreting the bend test data. However, in this case, the major advantage of the bend test, namely, simplicity, is eradicated.     

Creep and stress relaxation of germanium single crystals

Isothermal creep and stress relaxation were studied in germanium single crystals oriented for double slip at 400 to 700? C under compressive stresses of 180 to 490 kgf cm^?2. The curves, S-shaped in both types of experiment, were compared with correspondingones derived from a stochastic model involving a spectrum of energy barriers to dislocation movement. Agreement was satisfactory for stress relaxation; discrepancies in the case of creep point to the difficulty of correlating creep and stress relaxation when an equation of state is inadequate as an approximation for representing the plastic response. Differences between predicted and observed behaviour are, however, of diagnostic value concerning the extent of dislocation multiplication and other structural changes.     

General time‐dependent C(t) and J(t) estimation equations for elastic‐plastic‐creep fracture mechanics analysis

This paper presents equations for estimating the crack tip characterizing parameters C(t) and J(t), for general elastic‐plastic‐creep conditions where the power‐law creep and plasticity stress exponents differ, by modifying the plasticity correction term in published equations. The plasticity correction term in the newly proposed equations is given in terms of the initial elastic‐plastic and steady‐state creep stress fields. The predicted C(t) and J(t) results are validated by comparison with systematic elastic‐plastic‐creep FE results. Good agreement with the FE results is found.     

海冰的粘塑性蠕变模型

本文将粘塑性理论用于海冰荷载分析,并将现有的一维蠕变方程推广到二维形式,采用非线性有限元方法计算了作用在一单桩结构上的最大静冰力。     

Ein neues Zeitstandgerät für Kriechversuche bei wechselnden Belastungen und Temperaturen

A New Instrument for Measuring Creep under Alternating Loading and Temperature Conditions. It is an established fact that plastics are particularly subject to creep, i. e. deformation over a period of time under load. Under practical conditions unchanged load and constant temperature are seldom realized. The deformations associated with changing mechanical loads cannot generally be derived from the results of ordinary creep tests. In order to be able to study creep behaviour of plastics under intermittent load conditions (i. e. a sequence of loading and unloading), a special instrument has been developed at the Austrian Plastics Institute. The period of time as well as the ratio of loading and unloading phase can be programmed within wide ranges. Creep tests at varying temperatures can also be carried out with this instrument. Under intermittent load very significant differentiation of deformation and fracturing behaviour depending on the polymeric structure has been observed. Comparison of results of ordinary creep with those under intermittent loading at constant temperature shows, that in the case of amorphous thermoplastics destruction by stress crazing and fracture is markedly accelerated. On the other hand semicrystalline thermoplastics have excellent resistance against intermittent load.     

Observation of the relation between uniaxial creep and stress relaxation of filled rubber

This paper presents an experimental evaluation of the stress relaxation and creep of filled rubber. A detailed study of the influence of different test programs, where the main variable was the load sequence on the creep and relaxation processes, is discussed. The final goal of the research is to find a method to predict stress relaxation from known creep, or vice versa, in a simple way that would give sufficiently accurate results over both primary and secondary creep regions. Therefore suggestion for converting the creep test result into a stress relaxation curve and vice versa is presented. The idea is based on the assumption that both processes (creep and stress relaxation) are the result of the same viscoelastic mechanism and that the stress relaxation can be treated as creep under decreasing stress. Experimental data shows these assumptions to be correct. For the conversion of the creep parameters into stress relaxation parameters a reverse stress-strain curve is needed, therefore factors affecting the unloading stress-strain curve are also presented. Finally, the transition from the suggested conversion to the final method will be discussed.     

Estimations of creep fracture mechanics parameters for through-thickness cracked cylinders and finite element validation

This paper compares engineering estimation schemes of C* and creep crack opening displacement (COD) for cylinders with circumferential and axial through‐thickness cracks at elevated temperatures with detailed 3D elastic‐creep finite element results. Engineering estimation schemes include the GE/EPRI method; the reference stress (RS) method where the reference stress is defined based on the plastic limit load; and the enhanced reference stress (ERS) method where the reference stress is defined based on the optimised reference load, recently proposed by the authors. Systematic investigations are made not only on the effect of creep‐deformation behaviour on C* and creep COD, but also on effects of the crack location, the cylinder geometry, the crack length and the loading mode. Comparison of the finite element (FE) results with engineering estimations provides that for idealised power law creep, estimated C* and COD rate results from the GE/EPRI method agree best with FE results, suggesting that published plastic influence functions for plastic J and COD for through‐thickness cracked cylinders are reliable. For general creep‐deformation laws where either primary or tertiary creep is important and thus the GE/EPRI method is hard to apply, on the other hand, the ERS method provides more accurate and robust estimations for C* and COD rate than the reference stress method. As these two methods differ only in the definition of the reference stress, the ERS method maintains benefits of the reference stress method in terms of simplicity, but improves accuracy of the estimated J, C* and COD results.     

Viscoplastic response and creep failure time prediction of polymers based on the transient network model

The nonlinear viscoelastic/viscoplastic response of polymeric materials is described by a new model based on previous works in terms of monotonic loading, stress–relaxation, and creep. In the proposed analysis, following a constitutive equation of viscoelasticity, based on the transient network theory, essential modifications are introduced, which account for the nonlinearity and viscoplasticity at small elastic and finite plastic strain regime. In addition, viscoplastic response is successfully analyzed by a proper kinematic formulation, which is combined with a functional form of the rate of plastic deformation. A three-dimensional constitutive equation is then derived for an isotropic incompressible medium. This analysis is capable of capturing the main aspects of inelastic response and the instability stage taking place at the tertiary creep, related to the creep failure. Model simulations described successfully the experimental data of polypropylene, which were performed elsewhere.     

Springback simulation of advanced high strength steels considering nonlinear elastic unloading–reloading behavior

The stress–strain response of some materials, such as advanced high strength steels, during unloading is nonlinear after the material has been loaded into the plastic deformation region. Upon reloading, the response shows a nonlinear elastic response that is different from that in unloading. Therefore, unloading–reloading of these materials forms a hysteresis loop in the elastic region. The Quasi-plastic–elastic model (Sun and Wagoner, 2011) was modified and combined with both isotropic-nonlinear kinematic hardening and two-surface plasticity models to simultaneously describe the nonlinear unloading response and complex cyclic response of sheet metals in the plastic region. The model was implemented as user-defined material subroutines, i.e. UMAT and VUMAT, for ABAQUS/Standard and ABAQUS/Explicit finite element codes, respectively. Uniaxial loading-unloading tests were performed on three common grades of automotive sheet steel: DP600, DP980 and TRIP780 steel. The model was verified by comparing the predicted material response with the corresponding experimental response. Finally, the model was used to predict the springback of a U-shape channel section formed in a plane-strain channel draw process. The results showed that the model was able to considerably improve springback predictions compared to the usual assumption of linear elastic unloading.     

Nonlinear constitutive equations for transient creep of viscoelastic polymers including the effect of hydrostatic pressure

The behaviour of polymers is known to be significantly influenced by the hydrostatic pressure in creep deformation or elastic-plastic deformation. The effect of the third stress invariant on the nonlinear viscoelastic deformation is much smaller than that of the hydrostatic pressure. In this paper, a constitutive equation for transient creep is proposed, which includes the effect of the hydrostatic pressure on the yield function. The creep and plastic strains or the creep strain rate converge to zero with increasing hydrostatic pressure. The proposed constitutive equation is in good agreement with the actual creep data of cellulose nitrate and cellulose acetate, under various combinations of superimposed tensile and hydrostatic loadings.     

On creep stresses in a Bridgman notched bar

An approximate analysis of creep stresses in a Bridgman notched bar is given. In the case of strongly nonlinear creep, the rigid-creep model can be used. Both tension and combined tension-torsion are considered. A triaxial tension takes place in the central part of the bar. The maximal axial stress decreases with increasing twist and increasing creep index. At moderate torque, the influence of torsion on the stress state in the central part of the bar is relatively insignificant.     

Das Kriechverhalten von stickstofflegierten,austenitischen Stählen mit erhöhter Festigkeit bei Raumtemperatur

The Creep Behaviour at Room Temperature of Higher Strength Austenitic Steels containing Nitrogen. The mechanical properties of special austenitic steels with increased Cr and Ni contents and N₂ content up to 0,35 % have been investigated. In the as-received condition i.e. annealed and water quenched, the 0,2 % offset yield strength of these steels ranges from 400 to 500 N/mm². However, regardless of these increased yield strengths, the stress-strain characteristics are the same as for conventional austenitic steels. Since first plastic deformations correspond to an applied stress equal to 50 % of the 0,2 % yield strength, in practical applications the creep behaviour of these steels may be significant. Therefore, the creep behaviour at room temperature of the base metals and weldments has been investigated to determine the influence of thermal and mechanical treatments after annealing. The elastic limit of airquenched steels is significantly higher than of water-quenched, even though the 0,2 % yield strengths are essentially the same. This different stress-strain dependence influences the creep behaviour of the steel. The cold working of these steels by plastic straining in both tension and compression results in a useful strain hardening effect only when the direction of applied stress is the same as the stress during cold working. When the direction of stressing was reversed, a considerable Bauschinger-effect was observed.