Probabilistic aspects of progressive damage in composite structures

Abstract

The effects and importance of incorporating probabilistic aspects of the progression of damage in the analysis of composite structures are assessed. Two specific cases of graphite/epoxy with centrally-located holes are considered: a [0/90/±45], laminate subjected to equal biaxial tension, and a [±15/0],, laminate subjected to uniaxial tension. The variation in the basic composite material strength values are used with the maximum stress criteria to assess the probability of occurrence of various damage modes by evaluating the cumulative distribution functions of the corresponding material strength parameters at various locations in the structure for a given state of damage and applied load. An average stress approach is used in assessing the occurrence of both in-plane damage and delamination. Two-dimensional and threedimensional finite element models are used to obtain stress fields. In-plane damage is simulated by setting in-plane elastic constants of damaged elements effectively to zero. Out-of-plane damage is simulated by setting out-of-plane elastic constants of elements in adjacent plies effectively to zero. The results demonstrate that consideration of probabilistic characteristics of damage progression allows for the possibility of many different damage progression scenarios for a single laminate configuration, including the possibility of damage initiation and propagation via different damage modes (both in-plane and out-of-plane, as well as coupling between the two) and in numerous different geometric locations. Four key items that affect the probabilistic progressive damage behavior of the structure are identified: the particular details of the material strength distributions, the redistribution of stresses caused by the occurrence of damage, the damage history of the laminate including the modes and locations of all previous damage, and the nonlinear nature of failure probability as a function of stress. Recommendations are given to address some key issues in expanding the work. These include nonsymmetry of damage initiation and progression, use of strain energy release rate in assessing delamination, use of various material property degradation models to simulate damage, and consideration of probabilistic aspects of other material properties.