非理想界面桥联理论及横向压缩下基体的应力集中系数

In order to predict failure behavior and ultimate strength of a fibrous composite only based on its original constituent material properties, the internal stresses in the constituent fiber and matrix must be accurately calculated. Moreover, input data for the in-situ strengths of the matrix must be defined upon its original properties, as the former are not measurable. The Bridging Model developed by the author of this project proposal is one of the few theories currently available which can be used to calculate internal stresses in the fiber and matrix of a composite subjected to any arbitrary load. However, the bridging model has been established based on a perfect bonding assumption for the fiber and matrix interface. Furthermore, only when the stress concentration factors in the matrix due to introduction of a fiber are determined, can the in-situ strengths of the matrix be available from its original counterparts. The purposes of this project proposal are in two folds. Firstly, the bridging model theory with an imperfect fiber/matrix interface will be established. Secondly, the stress concentration factor of the matrix in a composite subjected to a transverse compression will be derived. Very recently, by solving bridging equations correlating averaged stresses in the fiber and matrix of a CCA (coaxial fiber cylinder assembled within an unbounded matrix) model, exactly the same Mori-Tanaka-Eshelby bridging matrix with a perfect fiber/matrix interface bonding has been obtained by the author of this project proposal. The same approach will be employed in this project to derive a bridging matrix of an imperfect fiber/matrix interface for a composite with an unbounded matrix domain, as the stress fields in the fiber and matrix of a CCA model have been vastly investigated in the literature. The thus obtained bridging matrix will be used to benchmark the establishment of an elastic-plastic bridging matrix for a composite with an imperfect fiber/matrix interface. Through both experimental investigation and theoretical analysis for failure mechanisms of a composite under a transverse compression, the failure plane orientation will be precisely identified and the stress concentration factor in the matrix due to the transverse compression will be determined. With these two achievements, the basis for predicting a composite strength using independently measured fiber and matrix properties will be more soundly set up.

欲根据原始组分性能预报复合材料的破坏和强度，首先要正确计算纤维和基体中的内应力，其次须由基体的原始性能正确定义其现场强度输入数据，因为后者无法测量。桥联理论是目前少有的能计算任意载荷下纤维和基体中内应力的理论，但现有桥联理论建立在纤维和基体理想界面基础之上。只有确定了基体因添加纤维产生的应力集中系数，才可正确得到其现场强度。本项目有两个研究目的，一是建立非理想界面桥联理论，二是确定横向压缩下基体的应力集中系数。基于构造Mori-Tanaka-Eshelby桥联矩阵相同的CCA（同心圆柱）模型，在纤维和基体接触面上引入非理想界面条件，导出相应的无限大基体域桥联矩阵，再以此为参照创建有限基体域非理想界面弹-塑性桥联矩阵。通过对复合材料横向压缩破坏机理的实验表征和理论解析，准确确定横向压缩破坏面方程及基体应力集中系数，为实现由独立测试得到的纤维和基体性能预报复合材料强度这一梦寐以求目标夯实基础。

复合材料受任意载荷作用的破坏和强度问题，只有通过细观力学求出纤维和基体的内应力后才能解决。一个明显例证：复合材料破坏往往源自界面开裂，但要确定任意载荷下界面何时开裂，必须知道纤维和基体中的内应力才行，后者只能通过细观力学方法得到。然而，细观力学求得纤维和基体中的内应力后，与各自极限参数比对所确定的复合材料强度，却往往与实际相差巨大。根本原因在于，细观力学得到的是均值内应力，而复合材料破坏分析必须基于真实应力。纤维中的应力场均匀，其真实应力与均值应力相同；基体的真实应力，等于均值应力乘以相应的基体应力集中系数。本项目研究的最重要成果，是得到了基体受横向压缩、横向剪切、轴向剪切及界面开裂后的横向拉伸应力集中系数，完善了基体真实应力理论，只额外提供一个复合材料横向拉伸强度，就可确定任意载荷下界面何时开裂。 .复合材料中的基体应力集中系数，完全不同于经典：1、经典应力集中系数因材料或结构中有缺陷而生，基体的应力集中系数则总存在，即便复合材料中不含任何缺陷，开孔等缺陷引起的复合材料应力集中是一种宏观量，由孔附近纤维和基体共同承担，基体的应力集中系数是一种细观量，仅仅由基体承受；2、经典应力集中系数定义是“点应力除以外加应力”，基体应力集中系数定义是“线平均应力除以体平均应力”；3、通过有限元等求出材料或结构中每一点应力后，经典应力集中系数往往不起作用，而基体的应力集中系数则对复合材料性能计算起决定性作用。事实上，基体的应力集中系数，开启了求解各种复合材料破坏和强度问题的大门。.细观力学桥联模型与其他理论相比，优势明显，但现有桥联模型建立在纤维和基体界面理想基础上。本项目还研究建立起针对纤维、界面、基体三相介质复合材料的桥联模型。由于其它非理想界面如纤维和基体之间粘接很弱的弱界面，总可通过调整界面相的厚度和材料参数实现，本项目建立的三相介质桥联模型具有普适性。