受热弹性复合球体空化问题的分析

Analysis for Cavitation Problem of Elastic Composite Ball Heated

研究了由两种弹性固体材料组成的复合球体,在均匀变温场作用下的空化问题.采用了几何大变形的有限对数应变度量和Hooke弹性固体材料的本构关系,建立了问题的非线性数学模型.求出了复合球体大变形热弹性膨胀的参数形式的解析解.给出了空穴萌生时临界温度随几何参数和材料参数的变化曲线,以及空穴增长的分岔曲线.算例的数值结果指出:超过临界温度后空穴半径将迅速增大,并且空穴萌生时环向应力将成为无限大,这意味着如果内部球体是弹塑性材料,则会在空穴表面附近产生塑性变形而造成材料的局部损伤.另外,当内部球体材料的弹性接近于不可压时,复合球体可以在较低的变温下空化.

The cavitation problem of composite ball, composed by two elastic solid materials and in uniformtemperature,was investigated.The nonlinear mathematical model of the problem was established by using finite logarithmic strain measure for geometric large deformation and by employing Hooke law for elastic solid.Analytic solutions in the form of parameter were derived for thermal dilatation of the composite ball with large elastic deformation.Solution curves were given to describe variations of the critical temperature in cavitation with the geometric and material parameters.Bifurcation curve was also given to reveal cavity growth after void nucleation.The numeric results for a computational example indicated that radius of cavity would rapidly enlarge over critical temperature,and the loop stress would become infinite with void nucleation.This means the materials near the cavity would produce plastic deformation which leads to local failure and fracture if the material of internal ball is elastoplastic.In addition,the cavitation for the composite ball could appear in a low temperature if elastic property for the material of internal ball is close to be uncompressible.