含片状缺陷共晶复合陶瓷的细观强度模型

Microscopic strength model for eutectic composite ceramics with platelet defects

根据缺陷在共晶复合陶瓷中的分布特点,假设缺陷为片状、缺陷周围介质为横观各向同性,建立了含缺陷共晶复合材料的细观力学模型;根据损伤理论定义了胞元等效外载应力场,依据等效夹杂理论得到了含缺陷各向异性基体复合材料Griffith强度,考虑缺陷的空间分布随机性得到了复合材料强度与缺陷尺寸、缺陷体积含量等参数的关系。结果表明:强度与缺陷半径的-1/2次方成线性关系,且缺陷尺寸较小时强度变化明显;片状缺陷体积含量对强度影响显著,尤其当缺陷含量小于3%时,少量缺陷即可造成强度极大地下降;缺陷形状及基体的各向异性对强度也有着重要影响,各向同性基体中片状缺陷不为圆形时,缺陷始终从短轴开始扩展,各向异性基体中片状缺陷为圆形时,则缺陷首先从弹性模量大的方向上扩展,最终缺陷形状和弹性模量满足特定的比例关系。

According to the distribution feature of inherent defect in eutectic ceramics,a relevant micro-mechanic model is established.Defects are assumed to be platelet,and matrix around is transversely isotropic.Effective stress field is obtained based on damage theory,and Griffith strength of anisotropic material is obtained based on equivalent inclusion method.By considering the random tropism of defects,the relationship between defect size,defect fraction and strength is analyzed.Result obtained indicates that strength and reciprocal of defect radius’s quadratic root reveals liner relation.The strength reduces as defect size increase and this reduction is sharp especially when the defect is small.Defects fraction has significant influence on strength also,a little fraction change may cause composite strength reduce rapidly as the fraction is lower than 3%.Anisotropic property of matrix has great influence on defect extending,and defect always extends from the smaller axis in isotropic matrix while it will extend from the axis of greater elastic modulus for penny shaped defect in anisotropic,and finally the defect shape and elastic modulus keep the specific proportional relation under simple tension condition.