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A straightforward failure theory based on the strengths of the fibre, matrix and interface makes it possible to predict composite failure and life directly. An easy-to-use preliminary design tool in Super Mic-Mac provides composite engineers with a powerful personal productivity tool.
(Published on June 2008 – JEC Magazine #41)
STEPHEN W. TSAI, PROFESSOR RESEARCH EMERITUS, DEPARTMENT OF AERONAUTICS AND ASTRONAUTICS, STANFORD UNIVERSITY
The traditional building block approach based on ply properties can now be replaced by micromechanics of failure (MMF), a constituent-based methodology for predicting failure and life of composites. The six starting strengths are four tensile and compressive strengths for the fibre and matrix, and two normal and shear strengths for the fibre/matrix interface. Micro-stresses in the matrix, fibre and interface are calculated from macro-level stresses using a micromechanics approach. Matrix and fibre constituent failures and interfacial cohesion damage are taken into account to determine the failure envelope of a unidirectional ply. The result is shown in figure 1.
There are many advantages of MMF: 1) fewer constants and assumptions, 2) clear identification of failure modes, 3) better agreement with data, and 4) simple extension to time-temperature dependent strengths from which life prediction can be made.
The epoxy matrix material is viscoelastic. Its time-temperature dependent properties can be defined on the basis of the storage modulus measured by dynamic mechanical analysis (DMA), from which a master curve can be formulated by shifting the data taken at different temperatures and rates. Figure 2 shows the master curve for the storage modulus (top) and its shift factor (bottom). The material is Hexcel 8552 epoxy.
Master curve of matrix strength
From the shift factor in figure 2, we can generate the master curve of the tensile strength for the 8552 matrix Tm with a reference temperature of 25°C (figure 3). We can generate a master curve for the matrix tensile strength by measuring the strength at four temperatures: 25, 50, 100, and 150°C.
The temperature-dependent strength is shown in the middle of figure 3. To the left is the shift factor. At 100°C, the shift factor for this matrix will be E-06. Thus, for the master curve, the 100°C tensile strength will have to be shifted to the left by six decades. This is shown on the right part of the lower char of figure 3. The master curve is formed when the strength at 50°C and 150°C is also shifted according to its shift factor for each temperature.
Fatigue failure envelope
It is possible to generate the fatigue failure envelope of laminates using the fatigue master curves of the constituents. An example is shown in figure 4.
By combining MMF with master curves, constituent properties can be related to composite failure and life. The method is straightforward and the testing is routine. An upcoming book, Failure and Life of Composites, will include details of of MMF and software tools, and will be available for Composites Design Tutorial 3 and JEC/Asia in fall 2008.