Predicting residual stresses due to solidification in cast plastic plates

Abstract

Thermal processing is an economical and efficient way of manufacturing polymeric products. However, it suffers from an important side effect that may considerably affect product performance: during non-uniform cooling to room temperature, strains become 'frozen in' the material. These frozen in strains lead to undesirable distortions and residual stresses within the final product. This work is concerned with cast filled PMMA plates for domestic applications. In a typical casting process, the material is first polymerised at a high temperature and then cooled to the ambient temperature. After cooling, the plate has distorted to an extent dependent on the cooling conditions.A method has been developed for quantitative prediction of the distortions and consequent residual stresses caused by non-uniform solidification. A 'residual' temperature field is introduced, which provides the relationship between the thermal history and frozen in strains. When applied as an actual temperature distribution, it results in distortions and residual stresses. Laboratory tests indicative of the actual casting process validated the frozen in strain model. Preheated plates were cooled in a controlled environment while temperatures were recorded at a number of locations on the plate surfaces. The measured temperature histories were then used in the numerical prediction of the residual temperature field. Experimental and numerically predicted distorted shapes agree very well.

Prediction of Residual Stresses in Injection‐Molded Plates Using the Residual Temperature Field Concept

“…By knowing the residual temperature field T res , the residual stress distribution can be calculated. Therefore, the key point in the residual stress analysis is the determination of the residual temperature field , which according to Eq. 15 is formed by the integration of the temperature gradients at the moment of solidification.…”

“…At time t + dt , the solidification front moves toward the interior of the plate, and the layers of softened material at the interface at time t are now in the solid region. A volumetric increment of frozen‐in strain Δε fr has been generated . This strain will remain locked in the material at the end of cooling.…”

“…These orthogonal lines will be the integration paths for obtaining the residual temperature field, T res , and the frozen‐in strains. According to Tropsa et al , the frozen‐in strain can be expressed as: where …”

“…The following analysis is based on the previous work of Tropsa et al [13,14], who extended the thermoelastic analysis of Williams [16] to predict residual stresses accounting also for anelastic effects. A large plate of thickness 2L is considered.…”

Experimental and numerical investigation of barreling at the cut ends of solid and skinned PE pipes

“…To calculate the residual stresses in the pipe, the temperature gradients at the moment of solidification are integrated to form the residual temperature field, . The residual stress distribution, , is calculated with the following equation [14] ( 2) where is the average value of through the specimen thickness, is the coefficient of thermal expansion, is the Poisson's ratio and the long term modulus of the material considering that after a long time at room temperature the relaxation modulus becomes equal to (240 MPa).…”