Printed Wiring Board Warpage

A Design and Analysis Problem

1. Introduction

Printed Wiring Boards (PWBs) are multilayer structures consisting of organic composites (such as FR4) and metallic circuit layers laminated together. Residual thermomechanical stresses from the curing process coupled with asymmetries of the laminate result in warpage, as well as more serious problems [Daniel et al., 1990]. This effect is exacerbated by further thermal cycles during component assembly processes such as solder masking and reflow soldering. The Finite Element Method (FEM) model of a typical PWB [Yeh et al., 1993] below illustrates what this deformation often looks like.

2. PBAM Tool to analyze this problem

Since the residual stresses which cause warpage are partly due to the coefficient of thermal expansion (CTE) mismatch between the materials in a PWB board, we may wish to search the reference books for other composite structures which warp due to mismatched CTEs.



One such structure is a bimaterial beam bending due to a uniform increase in temperature. Hence, we may wish to use this formula for a first order analysis of PWB Warpage.

Warpage =

In fact, if the analysis variables are selected correctly, it turns out that this simple model captures the maximum warpage wherever it occurs on the PWB! (For further details, examine our Analysis Model Explanation page.) For example, to model the board Yeh et al. analyzed with FEM (illustrated at the top of the page) the figures for the 'input' variables are:

Undeformed (i.e. initial) Length L = 276 mm
Undeformed Thickness t = 1.08 mm
Temperature Change = 70 ºC (from 25º to 95ºC)
Specific Coefficient of Thermal Bending = 1.10x10^-7/ºC (from 25º to 95ºC)

Since the formula does not predict the direction of the warpage, the resultant warpage figure (approximately 0.58 mm) represents the following PWB configurations: (warpage greatly exagerated for clarity)

Saddle Deformation	Bowl Deformation

This first order analysis example illustrates how an analysis model (which we call the thermal bending model) can be associated with a product (the PWB) to produce useful tool for designers and analysts.

This utility of associativity between a product model and an analysis model is one of the fundamental concepts behind Product-Based Analytic Models (PBAMs). We have therefore implemented this Thermal Bending Analysis as a PBAM based tool for evaluating PWB Thermal Warpage. The following pages provide further details of both the analysis model and the implementation details. We hope that these pages will provide you with both an introduction to the utility of PBAM-based tools, and a thorough exposition of the Thermal Bending Analysis Tool.

3. Where do I go from here?

To learn more about Thermal Bending Analysis, click here.

To see some of the specifications and implementation details of:

• The PWB Product Model, click here.
• The Thermal Bending ABB, click here.
• The PWB Thermal Bending PBAM, click here.

To view our reference sources, click here.

To begin analysis with this and other analysis models, first upload your STEP AP210 data file on our Data Upload Page.

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This page last modified on: February 18, 1997