Damage of structural materials under complex low-cycle loading

On the basis of the concepts of the continuum mechanics of damage, we propose an engineering method for the analysis of the kinetics of accumulation of scattered defects in metallic structural materials under conditions of elastoplastic deformation and low-cycle fatigue. It is shown that, in the general case of complex loading for the complex stress state, it is reasonable to use the specific energy of additional stresses (with regard for the arc of plastic strains in a loading cycle) as a parameter of damage for two types of fracture (rupture and shear). __________ Translated from Problemy Prochnosti, No. 6, pp. 25–34, November–December, 2007.     

Kinetics of scattered fracture in structural metals under elastoplastic deformation

The paper presents a procedure whereby the damage accumulation kinetics in structural materials, such as steel 45, stainless steel 12Kh18N10T, aluminum alloy D16T, and titanium alloy VT22, under elastoplastic deformation is studied based on variation parameters of elastic modulus and resistivity. For complex stress conditions, a continuum model for damage accumulation is proposed which relates the damage parameter to the intensity of accumulated plastic strains. The data calculated by the proposed continuum model are compared to the experimental findings of the investigation of the damage accumulation kinetics for some structural metals. __________ Translated from Problemy Prochnosti, No. 3, pp. 23–34, May–June, 2007.     

A method for low-cycle fatigue life assessment of metallic materials under multiaxial loading

A new method of fatigue life assessment under multiaxial low-cycle regular and irregular loading is proposed, which is based on the modified Pisarenko-Lebedev criterion, the linear damage accumulation hypothesis, and the nonlinear Manson approach. The results of low-cycle fatigue tests of titanium alloy VT9 under irregular proportional and non-proportional biaxial loading are given. The tests were carried out at three Mises strain levels (0.6, 0.8, and 1.0%) with various combinations of proportional and non-proportional strain paths. All the tests were carried out at room temperature. The proposed method turned out to be effective and to allow for such factors as strain state type, strain path type and loading irregularity. __________ Translated from Problemy Prochnosti, No. 1, pp. 56–59, January–February, 2008.     

Simulation of the proportional loading of elastoplastic materials simple in noll’s sense. Part 1. Defining relations

We postulate the invertibility of defining relations for hard materials that are simple in Noll’s sense. Representations of general physical equations for such solid bodies, including those with elastoplastic behavior, have been constructed in the conventional and inverse forms. Active proportional loading, primarily of isotropic materials, is simulated in detail for finite and infinitesimal strains of these solid bodies. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 3, pp. 56–68, May–June, 2000.     

An equation of state for porous materials under shock loading

Based on the physical interpretation of the linear equation of state (EOS) of dense solids under shock loading, which relates particle and shock speeds asU _s=C _b+gU _p, the EOS for porous solids has been developed and is expressed asU _s*=ΨC _b*+g*U _p whereC _b* andg* are effective bulk sound speed and effective inverse ultimate volume strain respectively. Ψ is a pore collapse function introduced specially to differentiate loading and unloading behaviour.C _b* andg* are derived theoretically whereas Ψ is established empirically as Ψ=f(U _p,C _b). This EOS does not call for any experimentally established material constant to describe the effect of porosity. Also its ability to describe the unloading behaviour distinguishes it from the presently available equations of state.     

An interaction energy integral method for T-stress evaluation in nonhomogeneous materials under thermal loading

An interaction energy integral method is developed for the finite element evaluation of the T-stress in nonhomogeneous materials under thermal loading. A domain-independent integral expression for extracting the T-stress is proposed for nonhomogeneous materials even when the integral domain intersects the interface. Then it is set in the extended finite element method (XFEM) so that the T-stress can be solved with high accuracy and efficiency. Several representative examples are solved to show the validity and the domain-independence of the method. A crack problem in a functionally graded thermal barrier coating (TBC) is also analyzed. Finally, the influences of material continuity on the T-stress are investigated. It can be found that the discontinuity of both thermal expansion coefficient and Young’s modulus affects the T-stress dramatically.     

Analysis of boundary-value problems describing the non-isothermal processes of elastoplastic deformation taking into account the loading history

We discuss the theory and approximate methods for solving boundary-value problems of thermoplasticity in a quasi-static formulation when the process of non-isothermal elastoplastic deformation of a body is a sequence of equilibrium states. In this case, the stress-strain state depends on the loading history, and the process of inelastic deformation is to be observed over the whole time interval being studied. The boundary-value problem is stated as a non-linear operator equation in the Hilbertian space. The conditions that provide the existence, uniqueness and continuous dependence of the generalized solution on the applied loads and initial strains are defined. A convergence of the methods of elastic solutions and variable elastic parameters is studied to solve the boundary-value problems describing the non-isothermal processes of active loading taking into account the initial strains dependent on the deformation history and heating. __________ Translated from Problemy Prochnosti, No. 1, pp. 69–99, January–February, 2006.     

Life estimation for high-strength materials under cyclic loading in the multiaxial stress state

The life of high-strength materials under cyclic loading in the multiaxial stress state is experimentally estimated using the deformation-kinetic criterion. Translated from Problemy Prochnosti, No. 2, pp. 139–143, March–April, 2009.     

Simulation of fading path shape memory in the theory of simple materials with elastoplastic behavior and initial loading surface

A mathematical theory is proposed rigorous construction and specialization of constitutive relations for simple (in the Noll’s sense) strain-hardening elastoplastic materials with an initial loading surface and a fading path shape memory at the active deformation segment. Strains and symmetry type of the material are taken to be arbitrary. Physical equations are derived for materials with no path shape memory, with a weak fading memory, and with a fading memory of the nth order. Based on the proposed constitutive relations, physical equations are constructed for isotropic materials. In the context of the fading path shape memory, a definition of an elastic-perfectly plastic material is given. Assuming the condition of smallness of measures of strains throughout the entire “past” history, a theory has been developed for rigorous construction and specialization of constitutive relations for materials with a first-order fading path shape memory for infinitesimal strains. Special emphasis is placed on isotropic materials. __________ Translated from Problemy Prochnosti, No. 4, pp. 5–18, July–August, 2007.     

On the existence of thermomechanical surface in materials under nonisothermal repeated simple loading

The paper discusses the findings of the experimental study of deformation in steels of various grades in tension with interim unloading stages where the test temperature was varied. It is demonstrated that not for all the materials this deformation process is described by the hypothesis of thermomechanical surface. The authors propose a constitutive equation for the materials under repeated simple loading with variable temperatures. __________ Translated from Problemy Prochnosti, No. 5, pp. 16–26, September–October, 2006.     

Analysis of the stressed state of a circular thin-walled cylinder under complex loading and with nonlinear hardening of the material

The generalized differential equations of plastic flow for a material with nonlinear hardening are derived using the Prager kinematic model. An example of numerical analysis for stress variation under elastoplastic deformation of a thin-walled cylinder of a structural carbon steel is given for different elastoplastic material models. Translated from Problemy Prochnosti, No. 3, pp. 58–65, May–June, 2009.     

Simulation of the fading memory of the form of trajectory in the theory of simple materials with elastoplastic behavior. Part 2. Infinitely small strains

For the processes of deformation close to proportional and slightly different from the stress- and strain-free configurations, in which plastic strains are formed immediately after the application of loading and monotonically increase in the process of deformation, we develop a mathematical theory of rigorous construction and specialization of determining relations for hardening elastoplastic materials with fading memory of the first order form of trajectory. The strains are regarded as infinitely small. The type of symmetry of the material is arbitrary. We use the determining relations of the linear theory of elastoplasticity for finite strains established earlier by the author. The condition of smallness of the measures of strains for the entire history is accepted. Special attention is given to the case of isotropic materials. The conditions of reduction of the constructed relations to one of the existing versions of the endochronic theory of plasticity are established.Translated from Problemy Prochnosti, No. 6, pp. 87–98, November–December, 2004     

Extension of the modified Bai‐Wierzbicki model for predicting ductile fracture under complex loading conditions

The ductile fracture behaviour of metallic materials is strongly dependent on the material's stress state and loading history. This paper presents a concept of damage initiation and failure indicators and corresponding evolution laws to enhance the modified Bai‐Wierzbicki model for predicting ductile damage under complex loading conditions. The proposed model considers the influence of stress triaxiality and the Lode angle parameter on both damage initiation and the subsequent damage propagation. The model parameters are calibrated for C45E + N steel using a series of mechanical tests and numerical simulations. The enhanced approach is applied to the modelling of various mechanical tests under proportional and non‐proportional loading conditions and successfully predicts the ductile damage behaviour in these tests.     

The construction of constitutive relations for isotropic strain-hardening elastoplastic materials of the differential type of complexity <Emphasis Type="Italic">n</Emphasis>. Part 2. Infinitesimal strains

A method of specialization of the physical equations constructed earlier by the author for isotropic hardening elastoplastic materials of the differential type of complexity n for finite strains is developed within the theory of infinitesimal strains. With this method, a number of constitutive relations are derived in the form of the hierarchy according to the level of complexity of the material response to deformation. For n = 1, the conditions for the existence of a loading surface are established. Translated from Problemy Prochnosti, No. 4, pp. 29–47, July–August, 2009.     

Method for the evaluation of the service life under random loading based on the energy criterion of fatigue fracture

We propose a method aimed at the assessment of the service life of structural elements under random loads based on the energy criterion of fatigue fracture and the model of cyclic deformation of materials after overloading. The possibility of determination of the maximum amplitude of stresses according to the number of loading cycles prior to fracture is substantiated. The results of evaluation of the service life under conditions of uniform stressed state are compared with the experimental data obtained by Swanson, Raikher spectral hypothesis of summation of defects, and linear hypothesis of summation. The dependence of the right-hand side of the linear hypothesis equation on the dispersion of the random loading process is established. __________ Translated from Problemy Prochnosti, No. 2, pp. 82–97, March–April, 2008.     

Procedure and Setup for the Investigation of Composite Materials in Torsion at Temperatures up to 3300 K

A procedure and a setup are proposed for the investigation of strength properties of composite materials under torsion at temperatures of up to 3300 K in vacuum and in an oxidizing or inert medium. The setup is fitted with a system for the program heating of specimens to realize conditions that are close to the working conditions of the material. This makes it possible to carry out tests at a heating rate of about 500 deg/s with a uniform temperature field maintained along the specimen length.     

四探针电阻率微区测量改进的Rymaszewski法厚度修正

为了解决四探针技术在微区测量中不能测试较厚样品的问题,提出了一种厚度修正方法该方法基于镜像源理论,以样品的上下边界为镜面,反复镜像电流源得到无限系列镜像源．将这些镜像源所产生的电位对测试点的影响进行叠加,推导出利用改进的Rymaszewski方形四探针法进行电阻率测量时的厚度修正公式,又利用规范化拟合法得到了多项式．修正后的结果反映了样品的真实电阻率,实验结果验证了该修正公式的正确性,从而完善了改进的Rymaszewski方形四探针的微区测量方法,使该方法能够应用到实际的测量中,提高了其实用性．