R curves for energy dissipative materials

This paper focuses on the theoretical simulation of fracture and stable crack growth of specimens with non-local damage. The first law of thermodynamics allows the identification or definition of appropriate crack-driving forces. The results are compared with recent ideas on defining tearing resistance for uncontained yield through the energy dissipation rate. A hypothesis regarding the conversion of mechanical into thermal energies within the non-local damage region is formulated to model the fracture behaviour of energy dissipative materials with rising crack resistance characteristics. The material's capacity to develop non-local damage is assumed to decrease with the actual damage level. This decrease relates linearly with the remaining resources of the material in dissipating energy. The hypothesis, which proposes a square root function for theoretical J-R curves, is verified by the regression analysis of experimental data regarding a European round-robin test of different steels.     

THE LINEAR NORMALIZATION TECHNIQUE—AN ALTERNATIVE PROCEDURE FOR DETERMINING J-R CURVES FROM A SINGLE SPECIMEN TEST RECORD BASED ON LANDES' NORMALIZATION METHOD

An alternative approach for determining J-R curves from a single specimen test based on the normalization technique is proposed. The procedure requires only the load versus load-line displacement record and the final crack length in order to derive the J-R curve. The method has been applied to metal and polymers of various geometries and was verified by comparison with J-R curves obtained from potential drop and multiple specimen techniques.     

An iteration method for directly determining J-Resistance curves of nuclear structural steels

An iteration method has been developed for determining crack growth and fracture resistance curves (J-R curves) of nuclear structural steels from the load versus load-line displacement record only. In this method, the hardening curve, the load versus displacement curve at a given crack length, is assumed to be a power-law function, where the exponent varies with the crack length. The exponent is determined by an iterative calculation method with the assumption that the exponent varies linearly with the load-line displacement. The proposed method was applied to the static J-R tests using compact tension (CT) specimens, a three-point bend (TPB) specimen, and a cracked round bar (CRB) specimen as well as it was applied to the quasi-dynamic J-R tests using CT specimens. The J-R curves determined by the proposed method were compared with those obtained by the conventional testing methodologies. The results showed that the J-R curves could be determined directly by the proposed iteration method with sufficient accuracy in the specimens from SA508 and SA516 pressure vessel steels and their welds and SA312 stainless steel.     

APPLICATION OF A NORMALIZATION METHOD FOR DETERMINING J-R CURVES IN GLASSY POLYMER PVC AT DIFFERENT CROSSHEAD SPEEDS

Abstract— A new single-specimen testing method, the normalization method with the so-called LMN calibration function, based on the load separation principle and function calibrations from an individual test record, was used to construct J-R curves directly from load versus load-line displacement records without any additional on-line crack-length monitoring equipment. The research was done on CT-specimens of a glassy polymer PVC at different crosshead speeds ranging from 0.01 to 50 mm/min. The J-R curves evaluated from the normalization method are in good agreement with those from the conventional multiple-specimen testing method in the whole range of the tested crosshead speeds. The results demonstrated the applicability of the normalization method for developing J-R curves at different crosshead speeds in PVC. The crack initiation J -integral values, J _0.2, showed a two-regime dependence on the crosshead speeds in the tested crosshead speed range.     

Ein stochastisches,schadensmechanisches Versagensmodell für Komposite

A stochastic damage mechanics failure model of composites This paper focuses on the theoretical simulation of strength and failure of specimens with nonlocal damage. A concept is proposed for quantitative interpretation and prediction of nonlinear. nominal stress-strain curves of damaged materials like fine ceramics or intermetallic alloys. For that reason methods of damage mechanics and of probability theory are combined.     

R-Kurven von energiedissipativen Werkstoffen mit Schädigungszone. Teil 1: Energieumsatz am Riß

R-Curves of Energy Dissipative Materials Part 1: Energy Consumption at the Crack The paper deals with the way in which the energy balance should be formulated when nonlocal damage processes associated with energy dissipation accompany crack growth. The local energy balance is used to rearrange the relationships between the different energies consumed both in the process of material separation and due to nonlocal damaging around the crack tip. The first law of thermodynamics allows the identification or definition of appropriate crack driving forces. The results are compared with recent ideas of Turner on defining tearing resistance for uncontained yield through energy dissipation rate.     

A nonlocal lattice particle model for J2 plasticity

In virtue of their intrinsic integro-differential formulation of underlying physical behavior of materials, discontinuous computational methods are more beneficial over continuum-mechanics-based approaches for materials failure modeling and simulation. However, application of most discontinuous methods is limited to elastic/brittle materials, which is partially due to their formulations are based on force and displacement rather than stress and strain measures as are the cases for continuous approaches. In this article, we formulate a nonlocal maximum distortion energy criterion in the framework of a lattice particle model for modeling of elastoplastic materials. Similar to the maximum distortion energy criterion in continuum mechanics, the basic idea is to decompose the energy of a discrete material point into dilatational and distortional components, and plastic yielding of bonds associated with this material point is assumed to occur only when the distortional component reaches a critical value. However, the formulated yield criterion is nonlocal since the energy of a material point depends on the deformation of all the bonds associated with this material point. Formulation of equivalent strain hardening rules for the nonlocal yield model was also developed. Compared to theoretical and numerical solutions of several benchmark problems, the proposed formulation can accurately predict both the stress-strain curves and the deformation fields under monotonic loading and cyclic loading with different strain hardening cases.     

A nonlocal cohesive zone model for finite thickness interfaces – Part I: Mathematical formulation and validation with molecular dynamics

A nonlocal cohesive zone model is derived taking into account the properties of finite thickness interfaces. The functional expression of the stress–separation relationship, which bridges the gap between continuum damage mechanics and nonlinear fracture mechanics, depends on the complex failure phenomena affecting the material microstructure of the interface region. More specifically, the shape of the nonlocal cohesive zone model is found to be dependent on the damage evolution. On the other hand, damage is in its turn a function of dissipative mechanisms occurring at lower length scales, such as dislocation motion, breaking of interatomic bonds, formation of free surfaces and microvoids, that are usually analyzed according to molecular dynamics. Hence, the relationship intercurring between the parameters of the damage law and the outcome of molecular dynamics simulations available in the literature is also established. Therefore, the proposed nonlocal cohesive zone model provides also the proper mathematical framework for interpreting molecular dynamics-based stress–separation relationships that are typically nonlocal, since they always refer to a finite number of atom layers.     

A nonlocal computational homogenization of softening quasi-brittle materials

In this paper, a computational counterpart of the experimental investigation is presented based on a nonlocal computational homogenization technique for extracting damage model parameters in quasi-brittle materials with softening behavior. The technique is illustrated by introducing the macroscopic nonlocal strain to eliminate the mesh sensitivity in the macroscale level as well as the size dependence of the representative volume element (RVE) in the first-order continuous homogenization. The macroscopic nonlocal strains are computed at each direction, and both the local and nonlocal strains are transferred to the microscale level. Two RVEs with similar geometries and material properties are introduced for each macroscopic Gauss point, in which the microscopic damage variables and the macroscale consistent tangent modulus and its derivatives are obtained by imposing the macroscopic nonlocal strain on the first RVE, and the macroscopic stress is computed by employing the microscopic damage variables and imposing the macroscopic local strain over the second RVE. Finally, numerical examples are solved to illustrate the performance of the proposed nonlocal computational homogenization technique for softening quasi-brittle materials.     

On nonlocal residuals and fluctuations

The nonlocal residual is a novel physical quantity introduced in the nonlocal field theory of mechanics. In this paper, the nonlocal residual and some related problems are discussed. Firstly, a representative theorem of nonlocal residual is proved, in which the relation between the nonlocal residual and the spatial distributed fluctuation of the interaction among microstructures in materials is established. The existence of nonlocal residuals of body force, body moment and energy is investigated in detail based on the objectivity of the balance equations. To meet the requirements in physics, an eigen-scale parameter is introduced into the nonlocal kernel. And the properties of nonlocal kernel are then discussed. Finally, the nonlocal hyperelastic constitutive equation is deduced through the representation of the nonlocal residual of energy. Results show that the nonlocality of hyperelastic constitutive equation comes directly from the interaction potential among microstructures within materials.     

Influence of plastic deformation on single-fiber push-out tests of carbon fiber reinforced epoxy resin

In our study we present a procedure to measure and analyze single-fiber push-out force–displacement curves on carbon fiber reinforced polymers using a cyclic loading–unloading scheme. The measured cyclic force–displacement curves allow an energy-based evaluation of the interfacial failure, taking into account elastic, plastic and other dissipative energy contributions. Experimental and modeling results demonstrate that a deviation of the push-out curve from linear behavior does not correspond to crack opening but to a plastic deformation of the matrix. Evaluating the plastic energy yields a linear increase of the total plastic energy after a certain indenter displacement. This linear increase is attributed to stable crack propagation. Back-extrapolation of the linear part to zero total plastic energy using a linear regression yields the initiation of crack growth. It is concluded that for ductile matrix materials like polymers, a reliable interpretation of push-out data has to take into account plastic material deformation.     

Bruchmechanische Analyse des Zähigkeitsverhaltens von teilchengefüllten Thermoplasten

Fracture Mechanic Analysis of Toughness Behaviour of Filled Thermoplastics For determination of toughness properties of filled thermoplastics the instrumented Charpy impact test has been used. The interpretation of impact load-deflection curves has been carried out with modern concepts of fracture mechanics. The change of toughness with increasing filler volume can be described for particle filled composites with the help of the J-integral in a suitable mode. The influence of filler volume, filler dimension and matrix type on critical J-integral and COD on the initiation of instable crack growth was tested. With the help of a micromechanical model to describe failure processes taking account of energy dissipative processes it is possible to calculate fracture mechanical behaviour of filled thermoplastics.     

A localizing gradient damage enhancement with micromorphic stress-based anisotropic nonlocal interactions

This article presents a localizing gradient damage model with evolving micromorphic stress-based anisotropic nonlocal interactions. The objective is to model mesh independent fracture behavior of quasi-brittle materials, and to avoid the issues associated with the existing gradient-enhanced damage models. In the proposed model, an evolving anisotropic nonlocal interaction domain governs the spatial diffusive behavior, which helps to maintain a localized damage bandwidth during the final stages of loading. The anisotropy in nonlocal interactions is captured through an anisotropic gradient tensor, which defines the orientation of the diffusive interaction domain based on the principal stresses at a given material point. In this article, a smooth micromorphic stress tensor is utilized for the determination of principal stress states, to enforce a properly oriented interaction across the bandwidth of the damage process zone throughout the loading process. The proposed approach also enables the usage of low order finite elements without any oscillatory micromorphic or nonlocal equivalent strain response in the later stages of deformation. The accuracy and performance of the proposed model are demonstrated numerically in plane strain/stress for mode-I, mode-II, and mixed-mode loading conditions.     

Modelling large crack propagation: from gradient damage to cohesive zone models

Continuum Damage Mechanics and cohesive zone models are both prone to model large crack propagation inside quasi-brittle materials. Comparing the advantages of the formulations, the latter could be advantageously applied in cases where the crack path is known a priori while the former implicitly encompasses crack path prediction but requires more complex computations involving nonlocal interactions. In order to assess the acceptability of such a hierarchy for industrial studies, it is necessary that the predictions coincide quantitatively. Starting from a gradient damage model in a one-dimensional context, a cohesive law is derived as the asymptotic response of the damage model for vanishing nonlocal length scale. The cohesive law is hence independent of the nonlocal length scale, which is consistent with the fact that it ignores details characteristic of the ??best-estimate?? damage approach. Besides, the existence of such a limit ensures that the damage model is not much sensitive to a small nonlocal length scale, which then appears rather as a numerical regularisation parameter. A numerical comparison between the damage model and its asymptotic cohesive law is then carried out for large bi-dimensional crack propagation. The computed responses remain close to each other although some small discrepancies arise probably related to the damage spread resulting from the stress distribution in the vicinity of the crack tip: the hierarchy strategy is thus validated.     

Fatigue resistance of high-temperature alloys under cyclic temperature variation. Part 2. Method of strength and service life prediction under two-frequency nonisothermal loading

We propose a criterion of the limiting state of a metal under two-frequency nonisothermal loading. The fatigue curves that are calculated using the linear damage summation hypothesis for the studied materials and thermocycling regimes lie above the experimental curves, while the curves calculated using the proposed technique are in good agreement with experiment. Analysis shows that the described technique for calculating the service life and the fatigue limits of materials under cyclic nonisothermal loading is universal, effective, and fully adequate for engineering calculations.Translated from Problemy Prochnosti, No. 4, pp. 16–22, April, 1994.     

ESEM investigations for assessment of damage kinetics of short glass fibre reinforced thermoplastics - Results of in situ tensile tests coupled with acoustic emission analysis

The damage mechanisms of short glass fibre reinforced polypropylene (PP) and polybutene-1 (PB-1) materials were investigated. For this purpose, in situ tensile tests were conducted in the environmental scanning electron microscope (ESEM) while simultaneously recording the acoustic emission (AE). To be able to observe damage mechanisms directly during loading, notched specimens were used. This method allows the direct correlation of the recorded load - elongation data with observed damage mechanisms, as well as correlations with acoustic emission data. Hence, it is possible to describe the damage kinetics of short glass fibre composite.It was found that different bonding conditions of the two investigated materials result in different damage mechanisms as well as in different AE behaviour. For fibre reinforced PP with excellent bonding conditions of the fibres in the polymeric matrix, fibre fracture, slipping of fibres in the delamination area, debonding and pull-out with matrix yielding was observed. The determined AE parameter amplitude A_p and energy E_AE for the PB-1 material are lower because of the weak bonding of the fibres to the PB-1-matrix. Hence, energy dissipative damage mechanisms like pull-out with matrix yielding can occur only in a limited part of such materials.     

Evaluating a strain energy fatigue method using cyclic plasticity models

For the development of constitutive equations that describe the behaviour of materials under cyclic plastic strains, different kinds of formulations can be adopted. Recently, an energy‐based fatigue damage parameter has been developed to present energy‐fatigue life curves using a calculation of the total strain energy. In this study, the damage criterion is examined by calculation of the plastic strain energy from stress–strain hysteresis loops in the cyclic plasticity models under condition of multi‐axial fatigue. These cyclic plasticity models are the Garud multi‐surface model and the Chaboche nonlinear kinematic hardening model. The models are briefly explained and the general features of their computational procedure are presented. Then, the hysteresis loops of these models will be obtained and the fatigue lives are predicted and compared to experimental data by the ratio of predicted life to experimental life. Consequently, a weighting factor on shear plastic work is presented to decrease the life factors.     

Local and global instabilities associated with continuing crack extension in dissipative solids

The model developed here links microstructural and continuum mechanics aspects of the early stages of the fracture process occurring in dissipative solids. A variable size damage zone, endowed with a structure of its own determined by the microstructural parameters related to the material ductility and grain size, is incorporated into a moving dominant crack. Prior to and during the course of crack extension, the energy dissipation mechanisms of diverse nature are activated within the volume of the localized damage zone, providing a substantial contribution to the effective material toughness. A criterion for quasi-static crack based on self-similarity of the crack-tip region is used to set up a governing equation of motion. The stress-transferring ability of the damage zone depends on the separation distance created between the two opposite boundaries of the fractures zone, and it determines the history of a quasi-static crack development including the attainment of the terminal instability point. Although detailed information regarding the distribution of stress prevailing within the nonlinear zone is lacking, it is shown that certain plausible governing equations may be constructed and employed to define material resistance curve in sufficiently large specimens (within the so-called ssy range), which is then used to predict the onset of catastrophic fracture. Six different specimen configurations are considered and the pertinent macro-mechanical stability analysis is presented in detail. The class of materials susceptible to this type of analysis is not restricted by the usual LEFM or EPFM constraint. This revised version was published online in August 2006 with corrections to the Cover Date.