The reliability of Plated through holes (PTH's) is presented as "PTH life curves" which plot cycle to fail vs. temperature for the entire range of field, accelerated thermal cycling, and assembly reflow thermal exposures on a Printed Wire Board (PWB) or Laminate Chip Carrier (LCC). The curves represent years of testing with the Current Induced Thermal Cycle test (CITC) covering different resin systems, via constructions, and metal finishes. The curves reveal a number of critical factors in PTH reliability including the significant effect of Pb free reflows, resin system formulation, and copper plate chemistry on via life.The critical importance of the "assembly life" region of the life curves is presented along with E/SEM photos of a crack opening during a reflow cycle. A finite element model is developed for one of the PTH constructions in this paper to show the complementary use of Finite Element Analysis (FEA) with this approach, since a valid model allows extension of the life data to other design and stress variables. The FEA fatigue life calculations correlated well with the experimental life curves. Examples of cumulative damage life projections for a number of PWB and LCC cases are given using the life curves. Finally, the importance of aggressive monitoring of PTH quality with the CITC 220C test is discussed.
Traditional approach to micro-mechanical modeling uses in situ properties of ingredients, which are so fitted as to match predictions of the micromechanical analysis with the experimental in-plane shear response of a lamina for a particular value of fiber volume fraction. In situ properties thus derived, cannot, in general, be used with a different fiber volume fraction or a different micromechanical model. The study presented here is based on the premise that micromechanical models should be transparent and rational tools for obtaining composite properties. Therefore, an attempt is made to characterize the composite from the actual properties of the ingredients and accounting for the presence of thermal residual stresses, shear softening and micro cracking in the matrix throughout the loading history. Experimental comparisons show that a micro-mechanical model with a realistic representative volume element (RVE) and diligent accounting of matrix behavior provides good bounds on experimental response with consistent accuracy, when bulk material properties are used.
Accuracy and computational simplicity are both sine qua non for micro-mechanical models which would be candidates for incorporation in structural analysis treating combined nonlinearities. To date there are a number of micro-models and most of these employ either a square cell or a circular cell as the representative volume element. The present paper discusses the accuracy of typical micro-models belonging to either category. A simplified square cell model (SSCM) derived from elementary mechanics is presented and this model is shown to give results almost identical to those of Aboudi's method of cells (AMC). A finite element-based 3-phase cylindrical fiber model (FECM) is developed with the primary object of determining the stress variation at the micro-level and thus the initiation of local failure. This model is apparently the most accurate in the set of models considered in the paper. It is confirmed that the closed form expressions of Hashin and Rosen in conjunction with the expressions to determine the transverse shear modulus given by Christensen and Lo offer a viable approach to the determination of elastic constants. The AMC and SSCM too provide sufficiently accurate prediction of plastic constants. However for the determination of initial yielding under combined loading, a micro-model which gives the variation of stresses across the model is required. The problem of the prediction of first yield of a metal matrix composite is considered and the results of the FECM are compared with those of the simpler square cell models and the hexagonal array model of Dvorak. The square cell models fail in the prediction of the first yield in the context of stress states which are nearly hydrostatic. The present FECM model is seen to be very effective because of the uncoupling of harmonics in the solution process and promises to be an effective tool for the inelastic analysis of the composites.
Two competing micromechanical models, viz. a simple square cell model (SSCM) and a finite element-based cylindrical model (FECM) are studied in comparison to assess the discrepancies that exist between them in the prediction of nonlinear behavior of composites. As a first step, FECM presented earlier in the context of elastic material response is now extended to deal with material nonlinearity. Simplifications are suggested to achieve the double goal of accuracy and efficiency. The paper then illustrates and quantifies the discrepancies between FECM and SSCM in respect to a common source on nonlinearity in composites, viz. the shear softening of the matrix. Limitations of the currently popular approach of "tuning" an inherently simplified model using test data are pointed out and discussed.
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