Creep damage and life analysis of anisotropic materials

Summary  This paper provides a short survey of some recent advances in the mathematical modelling of materials behaviour under creep conditions. The tertiary creep phase is accompanied by the formation of microscopic cracks on the grain boundaries in such a way so that damage accumulation occurs. The paper is divided into three parts. Firstly, the damage state in a uniaxial tension specimen is discussed and the time to rupture calculated. The second part is concerned with the creep behaviour of materials in multiaxial stress. Because of its microscopic nature, damage generally has an anisotropic character even if the material was originally isotropic. The fissure's orientation and length cause anisotropic macroscopic behaviour. Therefore, damage in an isotropic or anisotropic material, which is in a state of multiaxial stress, can only be described in a tensorial form. Thus, tensorial constitutive and evolution equations have been developed. Some examples for practical use are discussed. Finally, some own experiments are mentioned which have been carried out in order to validate the mathematical modelling. Received 16 July 1999; accepted for publication 8 March 2000     

Computer simulation of creep damage at crack tip in short fibre composites

Creep damage at crack tip in short fibre composites has been simulated by using the finite element method (FEM). The well-known Schapery non-linear viscoelastic constitutive relationship was used to characterize time-dependent behaviour of the material. A modified recurrence equation was adopted to accelerate the iteration. Kachanov-Rabotnov's damage evolution law was employed. The growth of the damage zone with time around the crack tip was calculated and the results were shown with the so-called “digit photo”, which was produced by the printer. The project supported by the National Natural Science Foundation of China and the LNM of Institute of Mechanics, CAS     

Fatigue and damage tolerance behaviour of corroded 2024 T351 aircraft aluminum alloy

The fatigue and damage tolerance behaviour of pre-corroded 2024 T351 aluminum alloy specimens has been investigated and compared to the behaviour of the uncorroded material. The experimental investigation was performed on specimens pre-corroded in exfoliation corrosion environment and included the derivation of S–N and fatigue crack growth curves as well as measurements of fracture toughness. The fatigue crack growth tests were performed for different stress ratios R. To obtain reference material behaviour all mechanical tests were repeated under the same conditions for uncorroded specimens. For the corroded material an appreciable decrease in fatigue resistance and damage tolerance was obtained. The results of the experimental investigation were discussed under the viewpoint of corrosion and corrosion-induced hydrogen embrittlement of the 2024 aluminum alloy. The need to account for the influence of pre-existing corrosion on the material’s properties in fatigue and damage tolerance analyses of components involving corroded areas was demonstrated.     

Mechanical characterisation of a viscoplastic material sensitive to hydrostatic pressure

The present paper deals with the characterisation of the static mechanical behaviour of an energetic material all along its lifespan. The material behaviour is viscoplastic, damageable and sensitive to hydrostatic pressure. For such materials, existing models have generally been developed in the framework of transient dynamic behaviour. These models are not suitable for a static study. Therefore a specific experimental protocol and an associated model are developed. Characterisation is derived from both uniaxial compressive, tensile tests and triaxial tests. Plastic behaviour is described by means of a parabolic yield criterion and a new hardening law. Non-associated plastic flow rule and isotropic damage complete the model. The performance of the model is illustrated through the simulation of various loading paths.     

A dissipation-based control method for the multi-scale modelling of quasi-brittle materials

Multi-scale models based on computational homogenisation are nowadays developed for the simulation of complex material behaviour. The use of homogenisation techniques on finite-sized representative volume elements in the presence of quasi-brittle damage may lead to the presence of snap-backs in the macroscopic material response. A methodology to simulate this type of response in the multi-scale technique is proposed, based on the control of the dissipation at the mesoscopic scale. To cite this article: T.J. Massart et al., C. R. Mecanique 333 (2005).     

Identification of Material Damage Model Parameters: an Inverse Approach Using Digital Image Processing

A reliable prediction of ductile failure in metals is still a wide-open matter of research. Several models are available in the literature, ranging from empirical criteria, porosity-based models and continuum damage mechanics (CDM). One major issue is the accurate identification of parameters which describe material behavior. For some damage models, parameter identification is more or less straightforward, being possible to perform experiments for their evaluation. For the others, direct calibration from laboratory tests is not possible, so that the approach of inverse methods is required for a proper identification. In material model calibration, the inverse approach consists in a non-linear iterative fitting of a parameter-dependent load–displacement curve (coming from a FEM simulation) on the experimental specimen response. The test is usually a tensile test on a round-notched cylindrical bar. The present paper shows a novel inverse procedure aimed to estimate the material parameters of the Gurson–Tvergaard–Needleman (GTN) porosity-based plastic damage model by means of experimental data collected using image analysis. The use of digital image processing allows to substitute the load–displacement curve with other global quantities resulting from the measuring of specimen profile during loading. The advantage of this analysis is that more data are available for calibration thus allowing a greater level of confidence and accuracy in model parameter evaluation.     

损伤弹性材料的有效模量及本构关系

考虑了微裂纹之间的相互作用，利用随机熔断丝网络（Ｒａｎｄｏｍｆｕｓｅｎｅｔｗｏｒｋ）作为模型，模拟了脆性材料在外载荷作用下，其有效模量随损伤的演变行为，并考察了系统含损伤的本构关系。发现在损伤初期，有效模量和损伤具有线性下降关系；而在后期，由于损伤局部化，有效模量迅速下降，提出了一个有效模量随损伤变化的非线性关系。讨论了利用网络模型来研究材料含损伤本构关系的可行性和优越性。     

Local and non-local Gurson-based ductile damage and failure modelling at large deformation

The purpose of this work is the formulation, numerical implementation and initial application of a non-local extension of existing Gurson-based modelling for isotropic ductile damage and attendant crack growth. It is being carried out under the premise that void coalescence results not only in accelerated damage development (e.g., Needleman and Tvergaard, 1984), but also in damage delocalisation (i.e., via interaction between neighbouring Gurson RVE's). To this end, we proceed by analogy with the approach of Needleman and Tvergaard (1984) who replaced the Gurson void volume fraction f with a (local) effective damage parameter f^* in the Gurson yield condition to account for the effect of void coalescence on the material behaviour. In the current case, the role of f^* is taken over and generalised by an effective continuum damage field ν. A field relation for ν is formulated here in the framework of continuum thermodynamics. In the simplest case, the resulting relation is formally analogous to the inhomogeneous temperature equation in which void nucleation and growth represent (local) sources for ν and in which void coalescence takes place in a process zone whose dimension is determined by a characteristic material lengthscale. Analogous to temperature, then, ν represents an additional continuum degree-of-freedom here, resulting in a coupled deformation-damage field model. In the last part of the work, the complete model for coupled damage-deformation is implemented numerically using the finite-element method on the basis of backward-Euler integration and consistent linearisation. Using this implementation, the behaviour of the current extended Gurson-based damage model is investigated for the case of simple tension of an inhomogeneous steel block. In particular, the corresponding simulation results document quantitatively the dependence of the delocalisation of the model damage process and minimisation of mesh-dependence on the characteristic dimension of the damage process zone.     

Simulation of failure under cyclic plastic loading by damage models

The purpose of this work is to simulate the evolution of ductile damage and failure involved by plastic strain reversals using damage models based on either continuum damage mechanics (CDM) or porosity evolution. A low alloy steel for pressure vessels (20MnMoNi55) was chosen as reference material. The work includes both experimental and simulation phases. The experimental campaign involves different kinds of specimens and testing conditions. First, monotonic tensile tests have been performed in order to evaluate tensile and ductile damage behaviour. Then, the cyclic yielding behaviour has been characterized performing cyclic plasticity tests on cylindrical bars. Finally, cyclic loading tests in the plastic regime have been made on different round notched bars (RNBs) to study the evolution of plastic deformation and damage under multiaxial stress conditions. The predictions of the different models were compared in terms of both, the specimens macroscopic response and local damage. Special emphasis was laid on predictions of the number of cycles prior to final failure and the crack initiation loci.     

Rheological properties of gluten plasticized with glycerol: dependence on temperature, glycerol content and mixing conditions

The rheological behaviour of a gluten plasticized with glycerol has been studied in oscillatory shear. The mixing operation in a Haake batch mixer leads to a maximum torque for a level of specific energy (500–600 kJ/kg) and temperature (50–60 °C) quite independent of mixing conditions (rotor speed, mixing time, filling ratio). The gluten/glycerol dough behaves as a classical gluten/water dough, with a storage modulus higher than the loss modulus over the frequency range under study. A temperature increase induces a decrease of moduli, but the material is not thermorheologically simple. Glycerol has a plasticizing effect, which can be classically described by an exponential dependence. Mixing conditions influence the viscoelastic properties of the material, mainly through the specific mechanical energy input (to 2000 kJ/kg) and temperature increase (to 80 °C). Above 50 °C, specific mechanical energy highly increases the complex modulus. The aggregation of proteins, as evidenced by size-exclusion chromatography measurements, occurs later as the dough temperature reaches 70 °C. The nature of network interactions and the respective influence of hydrophobic and disulphide contribution is discussed. A general expression is proposed for describing the viscous behaviour of a gluten/glycerol mix, which could seem simplistic for such a complex rheological behaviour, but would remain sufficient for modelling the flow behaviour in a twin screw extruder. Received: 24 November 1997 Accepted: 28 April 1999     

A new material model for concrete in high-dynamic hydrocode simulations

Summary  The development of material laws for concrete subjected to highly dynamic loadings is a topic of current research. Explosive charges or high-velocity impacts produce high pressures in the kilobar region within microseconds. Hydrocode simulations by coupling of Lagrangian with Eulerian grids have been carried out, considering the interaction between explosive loading and the structure. Concrete is a composite material with a variety of inhomogenities. By homogenization of the microstructure, a macroscopic approach in the framework of continuum mechanics has been adopted. Appropriate constitutive laws that enable the nonlinear rate-dependent as well as the local damage behaviour to be modelled had to be introduced. A new damage law that describes void compaction as well as the classical theory of plasticity had been taken into account. An equation of state had to be provided to ensure the compliance with conservation laws on which hydrocodes are based. To obtain the necessary material data, experimental investigations were indispensable. Therefore, a series of field tests with specimens which were concrete slabs exposed to explosive contact charges has been conducted. Received 19 March 1999; accepted for publication 9 December 1999     

Deformation and fracture of a spheroplast under low-cycle loading at various temperatures

This paper gives the results of an experimental study of the deformation and fracture of a spheroplast under uniaxial low-cycle loading (compression and unloading) at a temperature T = 25 and 100°C. Various mechanisms of damage accumulation at various temperatures and degrees of damage to the material are studied. The experimental results are compared with the well-known dependences taking into account damage accumulation for metals. It is established that the basic propositions of these theories are suitable for the low-cycle fracture of spheroplast — a ductile material of complex structure. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 197–204, January–February, 2009.     

Numerical experiments on the rupture of brittle solids––variation of microstructure,loading and dimensions

The significance of microstructural parameters for the damage and rupture of brittle materials is investigated by a numerical model that accounts for separation of grain interfaces. The microcracking approach refers to a specified material structure; synthetic random sampling allows for fluctuations. Thus, damage progression is simulated and the strength of material specimens is estimated by employing fracture mechanics within a microstructure that exhibits statistical variability. The issues addressed regard failure behaviour, strength level and sensitivity to microstructural parameters. Also discussed is the effect of specimen dimensions in connection with rupture.     

Lifetime simulation of thermo-mechanically loaded components

The estimation of the lifetime of thermo-mechanically loaded components by testing is very costly and time-consuming, since the high temperature cycle time in practical application dominates the test duration. Common frequencies for TMF (thermo-mechanical fatigue) tests are at about 0.01 Hz compared to 10–100 Hz at HCF (high cycle fatigue) and about 0.1–1 Hz at isothermal LCF (low cycle fatigue) tests. Therefore, the simulation of fatigue life is an important design step in the fast moving and competitive automotive industry, where the steady rise of engine power and the demand for lightweight construction concurrent with enhanced reliability require an optimised dimensioning process. Methods and models are usually derived from results made on tests with specimens, since it is possible to systematically and exactly define loading parameters and measurement categories. After an extensive test programme (tensile tests, creep tests, low cycle fatigue tests and thermo-mechanical fatigue tests with different influences on specimens) it was possible to develop material models for the simulation of the time- and temperature dependent stress–strain hystereses and damage models for the simulation of the TMF lifetime. Based on this knowledge the whole simulation chain to determine the TMF life of a component is introduced: thermal calculation, mechanical calculation and lifetime calculation. Furthermore the transferability of specimen based simulation models to real components (an alternative test piece and a cylinder head) is investigated.     

Analyzing methods to allow for the damage of material in thermoviscoelastoplastic deformation

Three methods to allow for damage of isotropic materials are discussed. The relations of the theory of deformation along paths of small curvature are used as equations of state. Rabotnov’s scalar equation is used to study the damage of a material during thermoviscoelastoplastic deformation. The stress determined by a stress rupture criterion that accounts for the stress mode is taken as an equivalent stress. An algorithm based on the finite-element method is developed to solve three-dimensional problems of thermoviscoelastoplasticity with allowance for material damage. The numerical results obtained are compared with experimental data __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 110–121, December 2007.     

Experimental study and modeling of damage of Al alloys using tensor theory

This article presents and evaluates experiments for the characterization and modeling of damage of structural aluminum and aluminum–magnesium alloys. Tensile tests were performed for specimens with artificial defects (voids) represented by different arrangements of pre-drilled micro-holes. The corresponding stress–strain curves were experimentally obtained. Plastic dilatation and deviatoric strain were determined both for the local zones with artificial defects and directly for meso-elements (i.e., material cells with artificial defects). A symmetric second-rank order tensor of damage was applied for a quantitative estimate of the material damage connected with the volume fraction and shape of micro-defects. The definition of this tensor is physically motivated, since its hydrostatic and deviatoric parts describe the evolution of damage connected with a change in volume fraction and shape of micro-defects, respectively. Such a representation of damage kinetics allows us to use two integral measures for the calculation of damage in deformed materials. The first measure determines damage related to an increase in void volume fraction (i.e., plastic dilatation). A critical amount of plastic dilatation corresponds to the moment of macro-fracture of the deformed metal. By means of experimental analysis, we can determine the function of plastic dilatation which depends on the strain accumulated by material particles under various stress and temperature-rate conditions of forming. The second measure accounts for the deviatoric strain of meso-elements, and is related to the change in their shapes. The critical deformation of ellipsoidal voids corresponds to the onset of their coalescence and to the formation of large cavernous defects. The second measure is considered as a criterion of micro-destruction due to formation of cavities in the deformed material. Based on the experimental data, some numerical modeling is realized for the investigated Al alloys to taken a change in stress triaxiality into account. It shows that a change in triaxiality toward smaller values results in an appreciable decrease of damage induced by strain. Both damage measures are important for the prediction of the meso-structure quality of metalware produced by metal forming techniques.     

An experimental investigation of composite repair

This study investigates the repair of a glass/vinylester composite material with damage caused by impact loading and bending. The repair technique is based on the “standard procedures” established in a previous study. In addition to the damage due to bending, the repair of composite plates with straight cutting-line damage is also investigated due to its similarity to the bending fracture and good repeatability for evaluation. It is found that two glass reinforcing patches of plain weave—that is, (0, 90)₂—on each side of the specimen can restore the original load-bearing capability of the composite material of concern. The investigation of the cutting-line damage can also be viewed as a study of bond-line angles for composite joining. It is concluded that a bond-line angle greater than 60° can restore the undamaged composite strength. In maintaining a large bond-line angle as well as a large bonding surface, various bond-line configurations are presented. Results from the five joints of V, W, WW, U, and UU shapes further verify this conclusion.     

Impedance-based non-destructive and non-parametric infrastructural performance evaluation

Among various non-destructive testing (NDT) techniques, the non-parametric impedance-based method using smart piezoceramic wafers to identify structural damage possesses the advantage of being independent of the detailed structural knowledge such as the geometry and material properties. This paper presents the experimental results showing the feasibility of using impedance-based NDT to identify damage in concrete—the important material used in many infrastructures.