Coefficient of cure shrinkage - A273

Coefficient of cure shrinkage
Foundational knowledge article
Document Type	Article
Document Identifier	273
Themes	Residual stress and dimensional control management
Relevant Class	Material
Tags	Material parameters Matrix Process modelling Thermoset polymers
Prerequisites	Basic Definitions of Material Properties

Introduction

The coefficient of cure shrinkage describes the volumetric change of the resin system during the curing process. For many thermosetting resins, this relationship is approximately linear within specific cure intervals, and the proportionality constant is called the coefficient of cure shrinkage.

Scope

This page defines the coefficient of cure shrinkage and outlines its significance in composite manufacturing. It will summarize how temperature and cure affect the development of strain within a part during the cure process. Also, typical ranges of this parameter for various resin systems are provided.

Significance

During the manufacturing of composite parts, resin shrinkage can introduce residual stresses within the system. The part may undergo deformation to relieve these stresses, commonly referred to as “spring-in”. This deformation is also influenced by the difference in the thermal expansion of matrix and reinforcement . These uneven thermal expansion coefficients and the cure shrinkage phenomenon lead to the development of internal residual stresses. The presence of these unintended internal stresses leads to a loss in dimensional accuracy and compromised longer-term performance and durability. As a result, an understanding of these principals are required when designing parts and their processing steps.

Prerequisites

Recommended documents to review before, or in parallel with this document:

• Polymer properties
• Degree of cure
• Gelation
• Coefficient of thermal expansion

Definition

During the curing process of a typical thermoset resin, the total volume decreases exclusively as a function of the degree of cure , this phenomenon is commonly referred to as cure shrinkage. As covalent bonds are formed between the chains, they are pulled closer and the proximity increases likelihood of more bonds being formed. Similarly in thermoplastic resins the process of crystallization causes volume shrinkage.

Process Dependencies

For the cure reaction to occur the resin must be heated, this increase or decrease in temperature also causes expansion or contraction of the matrix and reinforcement through thermal expansion. This creates a competing response at times in the cure cycle.

Cure shrinkage during gelation

The figure above illustrates the volumetric change of thermosets during the curing process. In the Pre-Gelation portion, from (a) to (b) the resin is a viscous liquid and hence expands by thermal expansion. Between (b) and (c), the volumetric change starts to be dominated by cure shrinkage, as the gelation point (c) is approached. In most cure cycles, the longest part of the cycle is the soak, which is when the part is held at a constant temperature. During the Cure development portion, the part undergoes the majority of the shrinkage. The Post-gelation portion of the cycle demonstrates the shrinking of the part as a result of the thermal expansion of the gelled resin. It is worth noting that the end point (e) is lower volume than the starting point (a).

It should be noted that the cure shrinkage is dominated by the matrix, and not the reinforcement in the composite. The fibers are much stiffer than the matrix, therefore in the fiber dominant direction cure shrinkage is often not appreciable. However, in the matrix dominant direction the part can shrink. For instance, unidirectional prepreg will not shrink in the direction of the fibers. However, in the transverse and thickness directions, the effects of cure shrinkage will affect the final dimensions of the part noticeably.

Gelation and cure Shrinkage

Gelation is the point at which the resin transitions from a viscous liquid to a rubbery state ; this occurs by increasing the crosslinking between polymer chains. This transition occurs at a constant degree of cure, that is independent of curing temperature . It is this transition from a viscous liquid to the solid that defines the modulus of the resin, and locks in internal stresses in the material .

During curing cycles of prepreg parts, temperature ramp and holds have different effects on the cure shrinkage. When the part is being held in a soak/hold, the temperature is held constant, the part undergoes cure shrinkage as the degree of cure increases. The relation between the strain over the degree of cure, which can be appreciated at this stage of the curing process, is referred to as the coefficient of cure shrinkage (CCS).

Cure shrinkage changes after gelation

Although the relationship between cure shrinkage and degree of cure is often thought of as linear , experimentally a non-linear behavior is observed. The non-linear characteristic of this relationship stems from the phase transition, carried forth by the gelation of the material. Specifically, the transition from liquid to rubbery solid through the crosslinking of the curing process directly affects the cure shrinkage as a degree of cure. As a result, to best represent the data, a piecewise linear best fit is proposed, in which a linear best fit is applied before and after the gelation of the thermoset.

Change in cure shrinkage coefficient before and after gelation

Typical Values

Total volume shrinkage of different resins from after fully cured.

• Polyester: 7-10%
• Epoxy: 2-8%

Measurement Method

To measure the CCS it is recommended to use a TMA. The TMA works by heating a sample and recording its displacements to a high accuracy. Another less common method is to place the sample on a heating stage and record it as it goes through a cure cycle and use Digital Image Correlation (DIC) which records a sample as it deforms, which a computer can analyze to get accurate displacements.

Experimental setup for measuring CCS

Related pages

Page type	Links
Introduction to Composites Articles
Foundational Knowledge Articles	Coefficient of cure shrinkage - A273 Coefficient of thermal expansion - A272 Conduction - A118 Convection - A106 Cure of thermosetting polymers - A162 Degree of cure - A104 Glass transition temperature (Tg) - A210 Heat of reaction - A114 Specific heat capacity - A117 Thermal conductivity - A116 Thermal diffusivity - A143 Thermal phase transitions of polymers - A102 Thermoplastic polymers - A161 Thermoset polymers - A105 Viscosity (resin) - A203
Foundational Knowledge Method Documents	How to measure curing time and degree of cure - M100 How to measure gel time - M101 How to measure reinforcement content (and corresponding matrix content) - M109
Foundational Knowledge Worked Examples
Systems Knowledge Articles
Systems Knowledge Method Documents
Systems Knowledge Worked Examples
Systems Catalogue Articles
Systems Catalogue Objects – Material
Systems Catalogue Objects – Shape
Systems Catalogue Objects – Tooling and consumables
Systems Catalogue Objects – Equipment	Rheometer - A357
Practice Documents	Ply Draping Modelling for Structural Analysis and Manufacturing - P174 Practice for developing a thermal transformation process step - P105
Case Studies	Improving Quality of a Truck Fender Using Ply Draping Modelling - C122 Troubleshooting of room temperature processes for large recreational and industrial parts - C100
Perspectives Articles	Case Study: Optimizing a Press Moulding Process - A324 Composite materials engineering webinar session 1 - Introduction - A120 Composite materials engineering webinar session 3 - Constituent materials - Resin - A122 Composite materials engineering webinar session 4 - Thermal management and resin cure - A123 Composites Process Simulation: A Review of the State of the Art for Product Development - A283 Dr. Anoush Poursartip's cdmHUB global composites expert webinar - A136 Fabric Forming: how it affects design and processing, and how simulation can address this - A310 Interview with Prof. Kevin Potter - A134 Simulation models for rapid liquid composite molding - A333.0 Understanding Polyester Resin Processing: The Effect of Ambient Temperature on the Final Part - A286

References

About	Help

For polymer matrix composites (PMCs), resin refers to the matrix; the continuous material phase that binds the reinforcement together, maintains shape, and transfers load. Resins are divided into two main groups: thermosets and thermoplastics.

Engineered materials (designed to have specific properties) made from two or more constituent materials with different physical or chemical properties. The constituents remain separate and distinct on a macroscopic level within the finished structure.

The continuous material phase that binds the reinforcement together, maintains shape, transfers load, protects the reinforcement from environment and damage, and provides the composite support in compression.

Desirable characteristics:

• Moisture/chemical resistance
• Low density
• Processability

Thermosets are a class of polymer that undergo polymerization and crosslinking during curing with the aid of a hardening agent and heating or promoter. Initially they behave like a viscous fluid. During curing, they change from viscous fluid to rubbery gel (viscoelastic material) and finally glassy solid.

If heated after curing, initially they become soft and rubbery at high temperatures. If further heated, they do not melt but decompose (burn)

Comes in two parts: part A (resin) and B (hardener). When mixed, curing reaction starts and is not reversible.

Examples include epoxy or polyester.

Degree of cure (DOC) is an indication of how far the chemical curing reaction (crosslinking process) has advanced in a thermoset resin.

DOC is defined with a number between 0 and 1 (or 0% and 100%) where 100% is a fully cured resin. It does not have to fully reach 100% for the resin to become solid or the part to be used. In some aerospace applications, resins are only cured to about 90%. Higher the degree of cure, higher the mechanical properties.

A class of polymer, some common examples include polypropylene and polyethylene.

They soften and melt upon heating (i.e. potentially recyclable), high viscosity when melted, therefore difficult to saturate fibres. Usually needs a lot of pressure and heat to process.

Pre-impregnated (prepreg) material refers to fibre that is already combined with resin. It is the most common material form used in aerospace.

During prepreg production, (e.g. fibres are run through a resin bath), prepreg is heated and partially cured to B Stage (< 5 % degree of cure). Thermoset prepregs (e.g. epoxy prepreg) have to be kept in a freezer at around -20 °C. At room temperature, the epoxy starts to cure.