Progressive damage modeling in fiber-reinforced materials

This paper presents an anisotropic damage model suitable for predicting failure and post-failure behavior in fiber-reinforced materials. In the model the plane stress formulation is used and the response of the undamaged material is assumed to be linearly elastic. The model is intended to predict behavior of elastic-brittle materials that show no significant plastic deformation before failure. Four different failure modes – fiber tension, fiber compression, matrix tension, and matrix compression – are considered and modeled separately. The onset of damage is predicted using Hashin’s initiation criteria [Hashin Z, Rotem A. A fatigue failure criterion for fiber-reinforced materials. J Compos Mater 1973;7:448; Hashin Z. Failure criteria for unidirectional fiber composites. J Appl Mech 1980;47:329–34] and the progression of damage is controlled by a new damage evolution law, which is easy to implement in a finite element code. The evolution law is based on fracture energy dissipation during the damage process and the increase in damage is controlled by equivalent displacements. The issues related to numerical implementation, such as mesh sensitivity and convergence in the softening regime, are also addressed.     

A study on estimation of damage accumulation of glass fibre reinforce plastic (GFRP) composites under a block loading situation

Many cumulative damage theories have been used in lifetime calculation of GFRP composite components. However, it is well known that linear damage accumulation models are inadequate for predicting the cumulative damage in GFRP compositeas due to their dominant viscoelastic characteristics. This paper discusses the outcomes of application of damage accumulation models proposed by Palmgren-Miner [Miner MA. Cumulative damage in Fatigue. J Appl Mech 1945;12(September):A159–64], Broutman and Sahu [Broutman LJ, Sahu SA. New theory to predict cumulative fatigue damage. In: Fiberglass reinforced plastics, composite materials: testing and design (second conference), ASTM STP 497; 1972. p. 170–88], Hashin and Rotem [Hashin Z, Rotem A. A cumulative damage theory of fatigue failure. J Mater Sci Eng 1978;(34):147–60] and Epaarachchi and Clausen [Epaarachchi Jayantha A, Clausen Philip D. On predicting the cumulative fatigue damage in glass fibre reinforced plastic (GFRP) composites under step/discrete loading. Composites Part A: Appl Sci Manuf 2005;36(9):1236–45], to calculate the lifetime of GFRP composite samples under repeated block loading situations.     

Numerical evaluation of shear strengthening performance of CFRP sheets/strips and sprayed epoxy coating repair systems

A numerical study is conducted to evaluate the shear strengthening performance of two repair systems: CFRP sheets/strips and a sprayed epoxy coating. Micromechanical constitutive models for the CFRP sheets/strips and sprayed FRP coating proposed by Liang et al. [Liang Z, Lee HK, Suaris W. Micromechanics-based constitutive modeling for unidirectional laminated composites. Int J Solids Struct 2006;43:5674–89] and Lee et al. [Lee HK, Avila G, Montanez C. Numerical study on retrofit and strengthening performance of sprayed fiber-reinforced polymer. Eng Struct 2005;27:1476–87] and Lee and Simunovic [Lee HK, Simunovic S. Modeling of progressive damage in aligned and randomly oriented discontinuous fiber polymer matrix composites. Composites: Part B 2000;31:77–86] in conjunction with damage models, are implemented into the finite element code ABAQUS to solve boundary value problems. Using the implemented computational model, numerical simulations of four-point bending tests on concrete beams repaired with the repair systems are conducted to quantify their strengthening abilities. The numerical tests yield load–deflection curves from which the shear strengthening performance of the repair systems is evaluated. Furthermore, the present prediction is compared with available experimental data to assess the accuracy of the proposed computational model.     

An RVE-based micromechanical analysis of fiber-reinforced composites considering fiber size dependency

An RVE-based micromechanical elastic damage model considering fiber size dependency is presented to predict the effective elastic moduli and interfacial damage evolution in fiber-reinforced composites. To assess the validity of the present model, the predictions based on the proposed micromechanical elastic model are compared with Hashin’s theoretical bounds [Hashin Z. Analysis of properties of fiber composites with anisotropic constituents. J Appl Mech: Trans ASME 1979;46:543–50]. The proposed micromechanical elastic damage model is then exercised under uniaxial loading conditions to show the overall elastic damage behavior of the proposed micromechanical framework and to illustrate fiber size effect on the behavior of the composites. Moreover, comparisons between the present prediction and experimental data are made to further illustrate the capability of the proposed micromechanical framework for predicting the elastic damage behavior of fiber-reinforced composites.     

Impact breach and fragmentation of glass plate

The present paper describes a first-order analytic model of the breach of monolithic glass plate subject to impact by chunky projectiles. The purpose of the model is to provide a theoretical framework for examining the consequences of the impact breach experiments of Sun et al. [Sun X, Khaleel MA, Davies RW. Modeling of stone-impact resistance of monolithic glass ply using continuum damage mechanics. Int J Damage Mech 2005;14:165-78]. A failure criterion of the Tuler-Butcher form [Tuler FR, Butcher BM. A criterion for the time dependence of fracture. Int J Fracture Mech 1968;4:431-7] is used with the model. The experimental impact breach experiments joined with the analytic model demonstrate time-dependent failure and lack of replica scaling for the present data. Methods are explored for the assessment of fragmentation resulting from the impact breach of brittle materials.     

Thermoelastic composites with columnar microstructure and cylindrically anisotropic phases. Part I: Exact results

A wide class of composite materials, which are in this paper referred to as having columnar microstructure, posses the microgeometrical characteristic that the constituent phases are homogeneous along one and only one direction. This class includes as an important subclass all the composites consisting of a homogeneous matrix reinforced by aligned parallel continuous homogeneous fibers. In the present work, considering a transversely isotropic composite with columnar microstructure and with cylindrically anisotropic phases, a number of exact results are established for effective thermoelastic moduli by modelling the composite as a nested composite cylinder assemblage. The results obtained in this work extend those of Hashin and Rosen [Z. Hashin, B.W. Rosen, The elastic moduli of fiber-reinforced materials, ASME J. Appl. Mech. 31 (1964) 223–232] and Hashin [Z. Hashin, Thermoelastic properties and conductivity of carbon/carbon fiber composites, Mech. Mater. 8 (1990) 293–308].     

A numerical study of fracture initiation in a ductile material containing a dual population of second-phase particles—II. Dynamic loading

Some recent experimental studies with pre-notched bend specimens of 4340 steel under both static loading [A. T. Zehnder and A. J. Rosakis, J. appl. Mech. 57, 618–626 (1990)] and impact loading [A. T. Zehnder et al., Int. J. Fracture 42, 209–230 (1990)] have shown that considerable crack-tunneling occurs in the interior of the specimens prior to gross fracture initiation on the free surfaces. The final fracture of the side ligaments happens because of shear-lip formation. The tunneled region is characterized by a flat fibrous fracture surface. In Part I of this work, the static experiments of A. T. Zehnder and A. J. Rosakis [J. appl. Mech. 57, 618–626 (1990)] were analyzed using a 2D plane-strain finite-element procedure. The constitutive model that was employed in this analysis accounted for the ductile failure mechanisms of microvoid nucleation, growth and coalescence. The simulation also modeled void initiation at two populations of particles of different sizes. In this part, the same constitutive model as in Part I is used, along with a plane-strain transient finite-element procedure to analyze the impact experiments reported by A. T. Zehnder et al., [Int. J. Fracture 42, 209–230 (1990)] corresponding to an impact speed of 5 m/sec. A direct comparison is made between the static and dynamic results regarding the development of ductile failure in the ligament connecting the notch-tip and a simulated inclusion ahead of it. It is found that, to attain the same level of microvoid damage in this ligament, a larger value of J is required under dynamic loading. The strain rate and adiabatic temperature rise near the notch-tip are also examined.     

Thermal and mechanical load induced damage behaviour of a low alloy steel: Mechanisms and modelling

A series of experiments, including macroscopic damage measurement and in situ microscopic observation at room temperature and tensile tests at eight different temperatures ranging from 20 to 900°C, is carried out. Mechanical load induced ductile damage evolution law and micromechanisms are presented, where damage evolution law is measured through a new a.c. potential system and the micromechanisms of damage and fracture are observed through an in situ technique in conjunction with a scanning electron microscope (SEM) equipped with a tensile platform. A continuum damage mechanics (CDM) model for ductile fracture proposed by Wang [Engng Fracture Mech. 42, 177–183 (1992)] is employed to model and to analyse the evolution law of damage in the steel. Comparison of experimental and modelling results is presented and good agreement is found. The effect of stress triaxiality on damage evolution is also discussed in the framework of CDM. The effect of temperature rise on tensile properties including Young's modulus, yield and ultimate tensile strength and ductility (elongation and reduction in area), is also reported.     

An experimental and numerical study of the effects of length scale and strain state on the necking and fracture behaviours in sheet metals

Within sheet metal forming, crashworthiness analysis in the automotive industry and ship research on collision and grounding, modelling of the material failure/fracture, including the behaviour at large plastic deformations, is critical for accurate failure predictions. In order to validate existing failure models used in finite element (FE) simulations in terms of dependence on length scale and strain state, tests recorded with the optical strain measuring system ARAMIS have been conducted. With this system, the stress–strain behaviour of uniaxial tensile tests was examined locally, and from this information true stress–strain relations were calculated on different length scales across the necking region. Forming limit tests were conducted to study the multiaxial failure behaviour of the material in terms of necking and fracture. The failure criteria that were verified against the tests were chosen among those available in the FE software Abaqus and the Bressan–Williams–Hill (BWH) criterion proposed by Alsos et al, 2008. The experimental and numerical results from the tensile tests confirmed that Barba's relation is valid for handling stress–strain dependence on the length scale used for strain evaluation after necking. Also, the evolution of damage in the FE simulations was related to the processes ultimately leading to initiation and propagation of a macroscopic crack in the final phase of the tensile tests. Furthermore, numerical simulations using the BWH criterion for prediction of instability at the necking point showed good agreement with the forming limit test results. The effect of pre-straining in the forming limit tests and the FE simulations of them is discussed.     

An FE-analysis of anisotropic creep damage and deformation in the single crystal SRR99 under multiaxial loads

Multidimensional stress–strain and damage analyses of engineering structural components with the help of numerical simulations are of great interest. These can only be done by using adequate material models and suitable numerical methods. Bertram and Olschewski (Computational modelling of anisotropic materials under creep conditions, Math. Modelling Sci. Comp. 5 (1995) 100–109; Anisotropic creep modeling of the single crystal superalloy SRR99, J. Comp. Mater. Sci. 5 (1996) 12–16), proposed a three-dimensional creep model for single crystals. An anisotropic creep damage model for single crystals was also suggested by Qi and Bertram (W. Qi, A. Bertram, Anisotropic creep damage modeling of single crystal superalloys, Tech. Mech. 17 (1997) 313–322; W. Qi, Modellierung der Kriechschadigung einkristalliner Superlegierungen in Hochtemperaturbereich, Ph.D. dissertation, Technical University Berlin, VDI Verlag, Düsseldorf, 1998; W. Qi, A. Bertram, Damage modeling of the single crystal superalloy SRR99 under monotonous creep, Comput. Mater. Sci. 13 (1998) 132–141). The coupled model has been used to predict the creep deformation and the lifetime of the single crystal SRR99 under uniaxial creep loads at 760°C. The purpose of this work is the application of the coupled model to the simulation of multiaxial creep behavior and damage development, and its dependence upon non-proportional loading paths of SRR99 at 760°C.     

Plane-stress crack-tip fields for pressure-sensitive dilatant materials

In this paper we present plane-stress crack-tip stress and strain fields for pressure-sensitive dilatant materials. A hydrostatic stress-dependent yield criterion and the normality flow rule are used to account for pressure-sensitive yielding and plastic dilatancy. The material hardening response is specified by a power-law relation. The plane-stress mode I singular fields are found in a separable form similar to the HRR fields (Hutchinson, J. Mech. Phys. Solids 16, 13–31 and 337–347, 1968; Rice and Rosengren, J. Mech. Phys. Solids 16, 1–12, 1968). The angular variations of the fields depend on the material hardening exponent and the pressure sensitivity parameter. Our low-hardening solutions for different degrees of pressure sensitivity agree well with the corresponding perfectly plastic solutions. An important aspect of the effects of pressure-sensitive yielding and plastic dilatancy on crack-tip fields is the lowering of the opening stress and the hydrostatic stress directly ahead of the crack tip. This effect, similar to that under plane-strain conditions (Li and Pan, to appear in J. Appl. Mech. 1989), has implications in the material toughening observed in some ceramic and polymeric composites.     

On modelling of damage evolution in textile composites on meso-level via property degradation approach

The continuous damage mechanics (CDM) approach is a popular tool for modelling of damage evolution in textile composites on the meso-level. It is based on the assumption that a material with defects can be replaced by a fictitious material with no defects but with degraded elastic constants. In such way the presence of defects is only reflected in the material elastic properties and damage evolution is recorded through the loss of these properties. The CDM approach incorporated into finite element analysis often predicts unphysically wide damage zones and in some cases failure across yarns – findings that are not supported by experimental data. The current work is geared toward identifying the source of inconsistencies between experiment and modelling by revisiting basic assumptions of CDM. A test problem is proposed to illustrate a break down of the CDM approach where a single crack-like defect in a yarn is modelled as an inhomogeneity with elastic constants reduced according to Murakami–Ohno model. It is shown that CDM in combination with local stress analysis of failure may predict a different direction of damage evolution as well as an incorrect failure mode in comparison with the crack problem. We also investigate whether the Murakami–Ohno model adopted for calculation of properties of a fictitious inhomogeneity contributes to the unphysical results. For this we compare contributions of a crack and an inhomogeneity into material elastic response. A new property degradation procedure is suggested (referred here as an effective elastic response model) where the size of an inhomogeneity and properties of the surrounding material are taken into account.     

Dynamic plastic response of circular plates in a damping medium

The motion of a simply supported circular plate of rigid-plastic material is studied. The motion is produced by a uniformly distributed impulsive velocity [Jones and de Oliveira, ASME J. appl. Mech. 47, 27–34 (1980)]. The material of the plate is assumed to obey the Tresca yield criterion with the inclusion of shear yield. The effect of damping by the surrounding medium on the plate motion is examined.     

An investigation of the damage mechanisms and fatigue life diagrams of flax fiber-reinforced polymer laminates

In this paper we investigated the fatigue damage of a unidirectional flax-reinforced epoxy composite using infrared (IR) thermography. Two configurations of flax/epoxy composites layup were studied namely, [0]₁₆ unidirectional ply orientation and [±45]₁₆. The high cycle fatigue strength was determined using a thermographic criterion developed in a previous study. The fatigue limit obtained by the thermographic criterion was confirmed by the results obtained through conventional experimental methods (i.e., Stress level versus Number of cycles to failure). Furthermore, a model for predicting the fatigue life using the IR thermography was evaluated. The model was found to have a good predictive value for the fatigue life. In order to investigate the mechanism of damage initiation in flax/epoxy composites and the damage evolution, during each fatigue test we monitored the crack propagation for a stress level and at different damage stages, a direct correlation between the percentage of cracks and the mean strain was observed.     

Constitutive modeling of void shearing effect in ductile fracture of porous materials

Many solids, including geomaterials and commercially available metallic alloys, can be considered as a porous media. The Gurson-like model has been proposed to describe plastic deformation for such type of materials. It has attracted a great deal of attention and various modifications to this model have been proposed. The constitutive equations of Gurson-like model are governed by the first and second stress invariants and the current void volume fraction of the material. Tvergaard and Needleman included void nucleation, growth and coalescence to Gurson model in a phenomenological way [Tvergaard V, Needleman A. Analysis of the cup-cone fracture in a round tensile bar. Acta Metall 1984;32(1):157–69] – thus suggesting the so called GTN model. Meanwhile, little attention was given to the dependence of the damage evolution on the third stress invariant. McClintock et al. [McClintock FA, Kaplan SM, Berg CA. Ductile fracture by hole growth in shear bands. Int J Fract Mechan 1966;2(4):614–27] proposed damage model based on the void evolution in localized shear banding. In the present paper, a separate internal damage variable which differs from the conventional void volume fraction is introduced. The GTN model is further extended to incorporate the void shearing mechanism of damage, which depends on the third stress invariant. Numerical aspects are addressed concerning the integration of the proposed constitutive relations. A unit cell is studied to illustrate the intrinsic mechanical behavior of the modified model. Computations of the deformation in axisymmetric and transverse plane strain tension are also performed. Realistic crack modes in these simulations are achieved for the modified GTN model.     

A failure criterion for brittle elastic materials under mixed-mode loading

The failure criterion of Leguillon at reentrant corners in brittle elastic materials (Leguillon 2002, Eur J Mech A/Solids 21: 61–72; Leguillon et al. (2003), Eur J Mech A—Solids 22(4): 509–524) validated in (Yosibash et al. 2004, Int J Fract 125(3–4): 307–333) for mode I loading is being extended to mixed mode loading and is being validated by experimental observations. We present an explicit derivation of all quantities involved in the computation of the failure criterion. The failure criterion is validated by predicting the critical load and crack initiation angle of specimens under mixed mode loading and comparison to experimental observations on PMMA (polymer) and Macor (ceramic) V-notched specimens.     

Micromechanical behaviour of Si-based particulate assemblies: A comparative study using DEM and atomistic simulations

In this paper, we investigate the micromechanical behaviour of Si-based particulate systems subjected to tri-axial compression loading. The investigations are based on three-dimensional discrete element modelling (DEM) and simulations. At first, we compare the variation of mean compressive stress for a silicon assembly subjected to tri-axial compression, predicted at two different scales: at the particulate scale, using the DEM simulation (mono-dispersed particulates) and at the atomistic scale using the molecular dynamics (MD) simulation results for silicon mono-crystal reported by Mylvaganam and Zhang (2003) [K. Mylvaganam, L. Zhang, Key Eng. Mater. 233–236 (2003) 615–620]. Both the simulation methods considered the silicon assembly subjected to an identical (tri-axial) loading condition. We observed a good qualitative agreement between the DEM and MD simulation results for the mean compressive stress when the assembly was subjected to small volumetric strain. However, at large volumetric strain, the mean stress of the silicon assembly predicted from MD simulation did not scale-up with the DEM results. This discrepancy could be due to that MD simulation is only valid for particle contacts, which are independent of one another and does not consider the inherent ‘discrete’ nature of particulates and the induced anisotropy prevailing at particulate scale. The micromechanical behaviour of particulate assemblies strongly depends on the inherent discrete nature of the particles, their single-particle properties and the induced anisotropy during mechanical loading. At the second stage, using DEM, we present the evolution of macroscopic compressive stress and several micromechanical features for four cases of the commonly used Si based poly-dispersed particulate assemblies (Si, SiC,Si₃N₄ and SiO₂) under tri-axial compression loading. We also present the evolution of several other phenomena occurring at particulate scale, such as the energy dissipation characteristics due to sliding contacts and the features of fabric structures developed during mechanical loading. The study shows that the single-particle properties of the Si based assemblies considered here significantly affect the micromechanical behaviour of the assemblies and DEM is a powerful tool to get insights on the internal behaviour of discrete particulates under mechanical loading.     

Fracture characteristics of Al/zircon particulate composites

A study has been made of the effects of volume fraction and size of zircon particulates on fracture toughness and micromechanisms of fracture in Al/zircon particulate composites. The composites are prepared by a liquid metallurgy technique using volume fractions of zircon in the range 0·06–0·18 and particulate sizes between 75 and 250 μm. The study was conducted on composites in the cast and the forged conditions. The experimental programme included a particle size distribution study, tensile tests, fracture mechanics tests leading to J_1c and crack tip opening displacement evaluation, fractographic investigations, etc. The process zone size at the crack tip was evaluated from crack tip stresses and strains, and compared with the interparticle spacing and particle diameter in order to understand the micromechanics of cracking. The Al/zircon composites were compared with Al/graphite composites in terms of strength and fracture toughness as a function of volume fraction of the filler phase, and regions of optimum performance were identified.