Effect of grain boundary sliding on creep constrained diffusive cavitation

For polycrystalline metals undergoing creep at high temperatures the nucleation, growth and coalescence of grain boundary cavities is investigated, with main focus on the influence of grain boundary sliding. Both the local stress state and the average rate of opening of a cavitating facet can be rather strongly affected by sliding on the grain boundaries emanating from the edges of this facet. A number of numerical solutions of axisymmetric model problems are used to study the combined influence of sliding and cavitation. The time to creep rupture by cavity coalescence is significantly reduced by grain boundary sliding, as is seen by comparison with analyses that disregard sliding. The numerical results are compared with predictions of a set of constitutive relations for creep in polycrystals with grain boundary cavitation.     

Analysis of the influence of aggressive environment on creep and creep rupture of rod under pure bending

Summary A method for modelling the influence of an aggressive environment on creep and creep rupture is suggested. This method is based on the introduction of a notion of structural elements and postulating elementary creep properties of these elements. The equations of behavior of a specimen as a whole are based on the behavior of the elements.A probabilistic approach is used for the analysis of creep and creep rupture of solids. Pure bending of a long thin rod in an aggressive environment is studied. It is supposed that the fracture of structural elements takes place only under tensional stresses. A system of integral-differential equations is derived; this system characterizes the process of damage accumulation and change of stress-strain state at times,which is caused by rod bending. It is demonstrated that rupture of any structural element in a tension area causes stress redistribution. This redistribution leads to a motion of the neutral lines at which stresses and strains equal zero. The numerical investigation of a derived system of equations is developed.This work has been partially supported by the Russian Foundation of Fundamental Researches (Grant No. 02-01-00289) and INTAS (Grant No. 03-51-6046).     

Creep rupture of specimens with random material properties

Possible sources of the observed scatter in creep deformation and rupture time are discussed. The scatter due to random material properties in creep is considered.A constitutive equation describing these random material properties is formulated. The rupture time of a specimen under constant load is calculated using Hoff s theory of ductile rupture. Rupture is shown to occur at finite elongation, in contrast to Hoff's original analysis.The probability distribution of the rupture time is determined with extremum value analysis and compared with experimentally observed ones.     

On a damage law for creep rupture of clays with accumulated inelastic deviatoric strain as a damage measure

To avoid the dependency on origin of time, an improved damage law for creep rupture of clays is proposed considering the accumulated inelastic deviatoric strain as a measure of damage, instead of incorporating time directly. This law is incorporated into an existing anisotropic elastoplastic-viscoplastic bounding surface model for clays. The performance of the damage law was demonstrated via the simulations of creep rupture tests on undisturbed clays, and generally a good agreement between model simulations and test data was obtained. Discussions on the creep rupture parameters were followed and further improvement was suggested. At present when high quality test data for creep rupture is very limited, the proposed damage law could serve as a practical way to model creep rupture of clays.     

Creep rupture under multi-axial states of stress

R are presented of metallographic examinations of specimens which have been creep tested at high temperatures and under different conditions of steady applied stress. The interaction between the growth of micro-fissures or voids and the mode of final rupture is discussed. The applied-stress versus rupture-life characteristics of a number of commercial alloys are presented together with simple expressions which are shown to describe approximately the stress-sensitive nature of their rupture behaviour.     

Influence of the cross-sectional shape of tensile bars on their creep rupture strength in a corrosive medium

The creep rupture strength of tensile bars in a corrosive medium is studied. The time to failure of the bars is analyzed as a function of their cross-sectional shape. It is shown that the influence of the corrosive medium on the creep rupture strength of the bars is determined by the diffusion of its elements into the bar material, resulting in a decrease in its creep rupture strength. The diffusion of the corrosive medium into a bar is studied using an approximate method for solving the diffusion equation taking into account the motion of the diffusion front. Bars with different cross-sectional shapes are considered using Rabotnov kinetic theory. It is shown that at the same tensile stress, the bar with a circular cross-section has minimum time to failure.     

Assessment of creep crack growth due to stress relief

An analysis is conducted to predict stress relief cracking at 550 °C in notched compact tension specimens of Type 316H austenitic stainless steel. The specimens had been subjected to pre-compression to generate a tensile residual stress distribution at the notch tip. This stress distribution is represented by a uniform reference stress over the zone of tension ahead of the notch tip. Creep rupture and creep crack growth data alone are required and used to make the predictions. It is found that the shape of the crack growth curve is correctly predicted when mean data are employed. However, upper bound crack growth properties are required to accurately predict the actual extent of cracking. Sensitivity studies show that the amount of stress relief cracking predicted is relatively insensitive to the reference stress initially assumed to describe the residual stress distribution, since the reference stress relaxes to a magnitude that is almost independent of its initial value. Adoption of an initial reference stress equal to the ultimate tensile strength of the steel, when combined with mean creep rupture and upper bound crack growth properties, results in safe predictions that are not overly conservative. The analysis should only be regarded as reliable for small amounts of crack extension of less than the size of the tensile zone ahead of the crack tip.     

Viscoelasticity and viscoplasticity of polypropylene/polyethylene blends

Observations are reported on polypropylene/polyethylene blends with various concentrations of components in uniaxial tensile tests with constant strain rates, relaxation tests, and creep tests at room temperature. A model is developed for the viscoelastic and viscoplastic responses of polymer blends at arbitrary three-dimensional deformation with small strains. Material constants in the constitutive equations are determined by fitting the experimental data. It is found that all adjustable parameters evolve with blend composition following an analog of the rule of mixture. Lifetime of blends under condition of creep rupture is evaluated by numerical simulation.     

SUS304材料的小冲孔蠕变试验研究

小冲孔蠕变试验技术是一种采用微小试样、近乎无损地评定材料高温力学性能的新方法,本文应用小冲孔蠕变试验技术评定SUS304材料的高温力学性能。在不同温度下,对SUS304奥氏体不锈钢进行载荷范围为443N～513N的小冲孔蠕变试验,得到材料在不同试验条件下的蠕变曲线,通过中断试样的扫描电镜观察分析了试样的变形过程,讨论了影响小冲孔蠕变试验的主要因素。试验结果表明,从小冲孔实验获得的蠕变曲线与传统单轴拉伸蠕变实验的蠕变曲线具有一致性,都具有三个明显的蠕变阶段,利用小冲孔蠕变试验技术测试材料的高温性能是可行的。试验载荷越大,试样瞬时变形挠度越大,蠕变第二阶段速率越快,断裂时间越短。载荷、温度、试样厚度、环境是小冲孔试验的主要影响因素,对试验结果影响很大。     

Nonlinear creep and ductile creep rupture of perfectly elastoplastic rods under tension

The paper is concerned with the problem of predicting nonlinear creep strains and time to ductile rupture of prismatic rods under constant tension. The material of the rod is assumed isotropic, homogeneous, and perfectly plastic. The problem is solved using models that take into account the change in the geometry of the rod during creep, the finiteness of the creep strains, and the effect of the initial and actual elastic strains. The conditions whereby the characteristic dimension of the rod tends to infinity and the accumulated and real strains in the viscous flow are limited are used as a failure criterion. The calculated results are compared with experimental data for a number of steels and alloys to formulate the conditions for the ductile rupture and embrittlement of metallic materials under uniaxial creep __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 4, pp. 120–133, April 2008.     

Damage of ductile materials deforming under multiple plastic or viscoplastic mechanisms

This work presents a model to represent ductile failure (i.e. failure controlled by nucleation, growth and coalescence) of materials whose irreversible deformation is controlled by several plastic or viscoplastic deformation mechanisms. In addition work hardening may result from both isotropic and kinematic hardening. Damage is represented by a single variable representing void volume fraction. The model uses an additive decomposition of the plastic strain rate tensor. The model is developed based on the definition of damage dependant effective scalar stresses. The model is first developed within the generalized standard material framework and expressions for Helmholtz free energy, yield potential and dissipation potential are proposed. In absence of void nucleation, the evolution of the void volume fraction is governed by mass conservation and damage does not need to be represented by state variables. The model is extended to account for void nucleation. It is implemented in a finite element software to perform structural computations. The model is applied to three case studies: (i) failure by void growth and coalescence by internal necking (pipeline steel) where plastic flow is either governed by the Gurson–Tvergaard–Needleman model or the Thomason model, (ii) creep failure (Grade 91 creep resistant steel) where viscoplastic flow is controlled by dislocation creep or diffusional creep and (iii) ductile rupture after pre-compression (aluminum alloy) where kinematic hardening plays an important role.     

Application of kinetic theory to the analysis of high-temperature creep rupture of metals under complex stress (review)

This paper gives an analytical review of the results obtained using the kinetic theory of creep and creep rupture to analyze the creep rupture of metals under complex stress. Special note is made of the outstanding contribution of Soviet scientists L. M. Kachanov and Yu. N. Rabotnov, who introduced the concept of material damage and developed the fundamentals of the kinetic theory. Different versions of this theory are used in studies of Russian and foreign scientists. The possibility of applying the kinetic theory to model the deformation and fracture of metals under creep conditions using scalar, vector, and tensor damage parameters and their combinations is considered.     

Experimental and Numerical Analysis of Initial Plasticity in P91 Steel Small Punch Creep Samples

To date, the complex behaviour of small punch creep test (SPCT) specimens has not been completely understood, making the test hard to numerically model and the data difficult to interpret. This paper presents a novel numerical model able to generate results that match the experimental findings. For the first time, pre-strained uniaxial creep test data of a P91 steel at 600 ^°C have been implemented in a conveniently modified Liu and Murakami creep damage model in order to simulate the effects of the initial localised plasticity on the subsequent creep response of a small punch creep test specimen. Finite element (FE) results, in terms of creep displacement rate and time to failure, obtained by the modified Liu and Murakami model are in good agreement with experimental small punch creep test data. The rupture times obtained by the FE calculations which make use of the non-modified creep damage model are one order of magnitude shorter than those obtained by using the modified constitutive model. Although further investigation is needed, this novel approach has confirmed that the effects of initial localised plasticity, taking place in the early stages of small punch creep test, cannot be neglected. The new results, obtained by using the modified constitutive model, show a significant improvement with respect to those obtained by a ’state of the art’ creep damage constitutive model (the Liu and Murakami constitutive model) both in terms of minimum load-line displacement rate and time to rupture. The new modelling method will potentially lead to improved capability for SPCT data interpretation.     

Comparative estimation of high-temperature creep and rupture of structural materials

The possibility of comparing the rates of creep processes and times to rupture of materials is shown by the example of several structural alloys of different types. The creep equation is written in dimensionless form, which allows one to compare creep processes up to rupture in normalized quantities, to estimate their difference, and, in the case of coincidence of the normalized quantities for some materials under corresponding temperature-load conditions, to model the indicated processes using experimental data for one of these materials. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 123–130, March–April, 2008.     

Non-linear creep damage under one-dimensional variable tensile stress

A non-linear damage relation, containing the axial strain history and a time integral over the stress history, is proposed for the case of one-dimensional time dependent tensile stress. Non-linear steady and transient creep terms are included in the axial strain relation, and elastic and creep Poisson's ratios are introduced into the lateral strain relation. Using these relations, complete damage solutions are obtained for the constant stress rate, step stress, relaxation and constant load tests. Observations are made concerning the associated rupture times.     

A non-linear viscoelastic model for ceramics at high temperatures

High-temperature mechanical behavior of ceramics is characterized by non-linear rate dependent responses, asymmetric behavior in tension and compression, and nucleation and coalescence of voids leading to rupture. Moreover, rupture experiments show considerable scatter or randomness in fatigue lives of nominally equal specimens. To capture the non-linear, asymmetric time-dependent behavior, a new non-linear viscoelastic model is proposed. Non-linearity and asymmetry are introduced in the volumetric component. To model the random formation and coalescence of voids, each element is assigned a failure strain sampled from a lognormal distribution. An element is deleted when its volumetric strain exceeds its failure strain. Temporal increases in strains produce a sequential loss of elements (a model for void nucleation and growth), which in turn leads to failure. Non-linear viscoelastic model parameters are determined from uniaxial tensile and compressive creep experiments on silicon nitride. The model is then used to predict the deformation of four-point bending and ball-on-ring specimens. Simulation is used to predict statistical moments of rupture lives. Numerical simulation results compare well with results of four-point bending experiments.     

A variational method for unidirectional fiber-reinforced composites with matrix creep

A variational method is developed for analyzing the matrix creep induced time-dependent change in fiber stress profiles in unidirectional composites. A functional of admissible profiles of fiber stress rate is presented by supposing a fiber broken in matrix as well as a fiber pulled out from matrix. The functional is shown to have the stationary function satisfying an incremental differential equation based on the shear lag assumption. Then, the stationary function is approximately determined by assuming bilinear profiles of fiber stress and a power law of matrix creep, leading to analytical solutions for the time-dependent change in fiber stress profiles. The solutions are verified on the basis of an energy balance equation and a finite difference computation. Moreover, it is shown that the solution for the fiber pull-out model agrees well with an experiment on a single carbon fiber/acrylic model composite if the initial slip at fiber/matrix interface is taken into account. In addition, the solution for the fiber breakage model is used for evaluating the characteristic time in long-term creep rupture of unidirectional composite.     

Prediction of creep rupture in 2.25Cr–1Mo notched bars

This paper re-examines the creep life methodology based on the continuum damage mechanics (CDM) of the Kachanov and Rabotnov theory. Uniaxial creep and multiaxial creep rupture formulations are presented taking into account the primary creep effect. The scalar damage parameter is computed up to time-to-rupture as a function of time and stress. The methodology implemented is based on the uniaxial time-to-rupture obtained experimentally. The times-to-rupture for bars with different notches are calculated. It is demonstrated that the use of the damage parameter is vital to indicate the critical damage location where failure occurs. Results are compared to those obtained experimentally. It is shown that the primary creep inclusion has a significant effect on the damage distribution zone.     

Results of studying creep and long-term strength of metals at the Institute of Mechanics at the Lomonosov Moscow State University (To Yu. N. Rabotnov’s Anniversary)

Basic results of experimental and theoretical research of creep processes and long-term strength of metals obtained by researchers of the Institute of Mechanics at the Lomonosov Moscow State University are presented. These results further develop and refine the kinetic theory of creep and long-duration strength proposed by Yu. N. Rabotnov. Some problems arising in formulating various types of kinetic equations and describing experimental data for materials that can be considered as statically homogeneous materials (in studying the process of deformation and rupture of such materials, there is no need to study the evolution of individual cracks) are considered. The main specific features of metal creep models at constant and variable stresses, in uniaxial and complex stress states, and with allowance for one or two damage parameters are described. Criterial and kinetic approaches used to determine long-term strength under conditions of a complex stress state are considered. Methods of modeling the metal behavior in an aggressive medium are described. A possibility of using these models for solving engineering problems is demonstrated.