Mechanisms-based creep constitutive equations for an aluminium alloy

Abstract

A number of mechanisms-based constitutive equations were assessed in an effort to describe the creep behaviour of an aluminium alloy at 150°C. It was found that a sinh function of stress, rather than the usually used power law, is best able to describe the strain rate and rupture behaviour over the narrow stress range analysed. A single state variable theory which represents a dominant damage mechanism is not capable of predicting the shape of the tertiary curve; however, a two state variable theory which represents two mechanisms provides a good description. The two relevant mechanisms identified are creep-constrained cavitation and ageing of the particulate microstructure.The non-linear equations which describe both these physical mechanisms are complex and strongly coupled. This makes it difficult to determine the constants in the constitutive equations from experimental data. The paper reports the development of automated numerical optimization techniques which overcome these difficulties.

A novel evolutionary algorithm for determining unified creep damage constitutive equations

“…Cauchy density function variables are introduced to accurately describe the deformation and damage mechanisms [1][2][3]. The determination of the values of material constants in such constitutive equations is often problematic, even when high quality experimental creep data is available [3,4].…”

“…The determination of the values of material constants in such constitutive equations is often problematic, even when high quality experimental creep data is available [3,4]. This di culty has been discussed by many researchers [1,4,5] and optimisation techniques are normally used to determine the material constants on the basis of minimising the sum of the errors between experimental and computed data.…”

“…However, for a set of uniÿed creep damage or general viscoplastic constitutive equations, numerical integration is needed for solving the equation sets. It has been shown that the objective functions for the optimisation are highly non-linear [3][4][5]. Hence, traditional gradient descent methods tend to fail because it is very di cult to choose starting values for the constants to obtain the global minimum.…”

“…Thus, extra care should be taken to choose starting values of the constants for optimisation. Kowalewski et al [3] developed a three-step method to determine the starting values of the constants in a set of creep damage constitutive equations for ÿnal optimisation. Perrin and Hayhurst [5] developed an optimisation method to determine damage constitutive equations based on a technique of transformation of creep constitutive equations.…”

“…First a set of uniÿed creep damage constitutive equations for aluminium alloys are introduced in Section 2. In order to avoid the traditional problem of the inconsistency in experimental and computed lifetimes [3], two new objective functions are formulated for this type of optimisation and the behaviour of the objective functions is then analysed in Section 3. Three evolutionary algorithms for minimising the two objective functions are described in detail in Section 4.…”