Brittle fracture in disordered materials: A spring network model
- PDF / 2,276,278 Bytes
- 19 Pages / 593.28 x 841.68 pts Page_size
- 0 Downloads / 285 Views
A model for investigating the influence of distributed disorder on the failure of brittle materials is introduced. The model assumes that microstructural features of a material can be represented by simple linear springs with a failure threshold, and that the entire material can be represented by a connected network of such springs. Distributed disorder is introduced by allowing spring-to-spring variations in spring characteristics such as the modulus and the failure strain. The conditions under which such a spring network model is valid for studying failure are discussed. The consequences of distributed residual stress disorder on macroscopic mechanical behavior are then studied using the network model, and a brittle to ductile-like transition in the stress-strain behavior is observed with increasing disorder. All the qualitative features of the network results can be described theoretically by a statistical analysis of this problem. Finally, notch tests are performed to evaluate the strength and toughness of the ductile-like materials as compared to the uniform (no disorder) material, and the ductile-like material is found to have (i) a larger work of fracture, (ii) comparable strength in the presence of processing flaws, and (iii) the possibility of larger toughness. Based on these results, the possibility of observing such ductile-like behavior in real composite materials is discussed.
I. INTRODUCTION
An in-depth understanding of the macroscopic and microscopic details of the mechanical failure of real materials is critical to the engineering of structural components and the design of advanced structural materials. Failure generally occurs by the growth of nucleated or intrinsic defects. And, in brittle materials, those materials exhibiting essentially no plasticity, the major defects are detected only when they cause precipitous failure. These materials are especially sensitive to the presence of intrinsic processing flaws (pores, cracks, etc.) occurring on length scales much smaller than the sample size because such flaws become unstable to unbounded growth at a critical stress with no indication of the incipient failure at lower stresses. Now, in addition to flaw populations, other "defects" can arise even in nominally polycrystalline single-phase materials. These defects are, for instance, variations in grain or grain boundary properties, which cause the failure to deviate from that of an ideal, uniform system (i.e., with uniform grain size, orientation, and boundaries). Rather than refer to these variations as defects, we will refer to the material containing them as disordered. The recent and rapid development of ceramic composites composed of a brittle matrix with brittle reinforcements presents many additional sources of distributed disorder, such as residual stresses, and different length scales on which the disorder may appear. In fact, by our definition, essentially all non-single-crystal materials are J. Mater. Res., Vol. 5, No. 3, Mar 1990
disordered in some manner. Some specific examples of dis
Data Loading...
