Analysis of Crack-tip Field of Particulate-Reinforced Composites Taking Account of Particle Size Effect and Debonding Damage

This paper deals with an analysis of a crack-tip field of particulate-reinforced composites which can describe the evolution of debonding damage, matrix plasticity and particle size effect on deformation and damage. Numerical analyses were carried out on a crack-tip field in elastic-plastic matrix composites reinforced with elastic particles by using a finite element method developed based on an incremental damage theory. The particle size effect on damage is described by a critical energy criterion for particle-matrix interfacial debonding. The effect of debonding damage on a crack-tip field is discussed based on numerical results. The debonding damage initiates and progresses ahead of a crack-tip. The stress distribution shifts downward in the debonding damage area. It is concluded that a crack-tip field is strongly affected by debonding damage. Introduction The technique to improve mechanical performance of materials by dispersing particles in a matrix has been applied to ceramic-matrix, metal-matrix and polymer-matrix composites, and these materials are called particulate-reinforced composites. A variety of damage modes such as fracture of particles and interfacial debonding between particles and matrix develop in the composites under external loading. These damage modes strongly affect mechanical performances such as stress-strain relation, tensile strength and fracture toughness [1, 2]. It is well known that mechanical performances also depend on particle size; the particle size is smaller, yield and flow stresses are more enhanced [3]. Tohgo et al. developed a constitutive model taking account of particle size effect and damage evolution and discussed the influence of debonding damage and particle size on overall stress-strain relation of composites [4]. Stress concentration area such as a crack, notch and edge in particulate-reinforced composites complicates their fracture behavior because debonding damage and matrix plasticity affect stress and strain field. To discuss the complex fracture behavior, a finite elemental analysis should be developed. In this paper, a finite element method based on the constitutive model by Tohgo et al. [4] has been developed. Numerical analyses of a crack-tip field under three point bending are carried out for composites containing various sized particles. Influence of debonding damage on stress field ahead of a crack-tip is discussed based on the numerical results. Incremental damage theory The incremental damage theory of particulate-reinforced composites is briefly explained [4]. The process of debonding damage of the composites can be simulated by the following assumptions. (1) The debonding of particles is controlled by the stress of the particles and the particle-matrix interfacial strength. (2) During debonding, the stress of the debonded particle is released and the site of the particle is regarded as a void. (3) A volume fraction of the debonded particles turns into a void volume fraction, and progressive damage in the composite is expressed by a decrease in an intact particle volume fraction and an increase in a void volume fraction. Figures 1 show the states of a composite undergoing damage process before and after incremental deformation. Figure 1(a) shows the state before deformation. The volume fractions of intact particles and debonded particles are expressed by fp and fd. If the volume fraction of the particles to be debonded in the incremental process is denoted by df, the volume fractions of the intact particles and the debonded particles will change to fp-df and fd+df after incremental deformation as shown in Fig. 1(b). For this incremental deformation, the constitutive relation is described by the form decomposed into the hydrostatic and the deviatric parts as follows: