Influence of Loading History on Delamination in Multilayered Beam with Creep

The present paper deals with an analytical study of the time-dependent delamination in a multilayered inhomogeneous cantilever beam with considering of the loading history. The multilayered beam exhibits creep behaviour that is treated by using a non-linear stress-strain-time relationship. The material properties are continuously distributed along the thickness and length of the layers. The external loading is applied in steps in order to describe the loading history. The analysis reveals that during each step of the loading, the strain energy release rate increases with time. The influences of crack length and location on the time-dependent strain energy release rate are also investigated.

Discrete Layer Jamming for Variable Stiffness Co-Robot Arms

Continuous layer jamming is an effective tunable stiffness mechanism that utilizes vacuum to vary friction between laminates enclosed in a membrane. In this paper, we present a discrete layer jamming mechanism that is composed of a multilayered beam and multiple variable pressure clamps placed discretely along the beam; system stiffness can be varied by changing the pressure applied by the clamps. In comparison to continuous layer jamming, discrete layer jamming is simpler as it can be implemented with dynamic variable pressure actuators for faster control, better portability, and no sealing issues due to no need for an air supply. Design and experiments show that discrete layer jamming can be used for a variable stiffness co-robot arm. The concept is validated by quasi-static cantilever bending experiments. The measurements show that clamping 10% of the beam area with two clamps increases the bending stiffness by around 17 times when increasing the clamping pressure from 0 to 3 MPa. Computational case studies using finite element analysis for the five key parameters are presented, including clamp location, clamp width, number of laminates, friction coefficient, and number of clamps. Clamp location, number of clamps, and number of laminates are found to be most useful for optimizing a discrete layer jamming design. Actuation requirements for a variable pressure clamp are presented based on results from laminate beam compression tests.

Analytical Study of Elastic-Plastic Fracture in the Crack-Lap Shear Multilayered Beam Configuration

This paper reports an analytical study of delamination fracture in the Crack-Lap Shear (CLS) multilayered beam configuration with taking into account the material non-linearity. A delamination crack was located arbitrary along the beam height. It was assumed that the CLS mechanical response can be described by using a power-law stress-strain relation. It should be mentioned that each layer may have different material constants in the stress-strain relation. Besides, the thickness of each layer may be different. The classical beam theory was applied in the present study. The non-linear fracture behaviour was analyzed by the J-integral. Analytical solutions of the J-integral were obtained for homogeneous as well as for multilayered CLS beams. In order to verify the solutions obtained, analyses of the strain energy release rate were developed with considering material non-linearity. Material properties and crack location effects on the non-linear fracture behaviour were investigated. The analysis revealed that the J-integral value increases when the material non-linearity is taken into account. It was found also that the J-integral value decreases with increasing the lower crack arm thickness. The approach developed here is very convenient for parametric fracture analyses. The solutions derived can be used for optimization of the CLS multilayered beams with respect to their fracture performance.

Effects of Build-Up Material Properties on Warpage Dispersion of Organic Substrates Caused by Manufacturing Variations

In large-die (20mm and above) flip-chip packaging applications such as high-end processors, the organic substrates have been widely used. In most cases, they are double-sided multi-layer printed wiring boards. The substrates mainly consist of glass-reinforced rigid core, build-up film resin layers and copper trace patterns. During chip attaching process, the substrates are warped due mainly to the unbalance in copper loading ratio of the build-up layers between the front and the back of the core layer. A common practice for minimizing the warpage of a substrate is to balance its copper loading as much as possible at its design stage. However, the thickness of each build-up layer and trace pattern can shift from its designed value due to fluctuation in process conditions during manufacturing. Consequently, the substrate warpage becomes larger than the minimized value, since the copper loading is no longer balanced. One of the possible solutions for this challenge is to minimize the errors in manufacturing process. Another solution is to make the substrates more resilient to the manufacturing variations. The latter can be performed at the design stage. The substrates can be made resilient by minimizing the warpage deviation when the thickness of the build-up layer and trace pattern are varied. In this paper, we have found that the warpage dispersion can be reduced by the build-up material properties which are the key components in balancing the front and back build-up layers. To study the effect of the build-up material properties, we performed dispersion analyses using the multilayered beam model. The analyses results showed a minimum in warpage dispersion when the coefficient of thermal expansion (CTE) of build-up materials is varied at a fixed Young’s modulus. They also show that the warpage dispersion decreases with decreasing Young’s modulus of build-up materials. The analyses are also done by Monte Carlo simulation with finite element analyses (FEA) so that the analyses can be applied to more complex substrates made for actual packages. The results of Monte Carlo simulations were consistent with those of obtained by the multilayered beam model. The values in build-up material for minimizing the warpage dispersion are in realistic range. In summary, we showed that the organic substrates can be made resilient to manufacturing variations by choosing build-up materials with appropriate material properties which minimize the warpage dispersion.