A novel constitutive model for multi-step stress relaxation ageing of a pre-strained 7xxx series alloy

Abstract

A novel set of unified constitutive equations has been developed and validated to describe stress relaxation ageing (SRA) behaviour. The model, based on dynamic ageing and power-law creep relations, can predict the stress relaxation, age hardening response and their interactions at different temperatures, through considering the microstructure evolutions (precipitate radius, volume fraction and dislocation density) during SRA. In addition, the model newly incorporates the effects of prior cold work. This model was verified through T74 multi-step SRA experiments for different pre-strain conditions. Excellent agreement was achieved between the predicted and experimental stress relaxation and yield strength evolutions. The evolutions of microinternal variables (e.g. normalised precipitate radius) within the model were calibrated by both the TEM results in this work and the experimental results from the literature. The model provides a valuable tool to predict the mechanical properties, and residual stresses post ageing, thus provides important guidance for designing manufacturing processes, leading to many benefits including reduced scrap rates and financial losses.

Stress Relaxation Aging Behavior and Constitutive Modelling of AA7150-T7751 under Different Temperatures, Initial Stress Levels and Pre-Strains

“…Therefore, the yield strength in this state is slightly lower than initial state. Ma et al and Zheng et al [13,14] also demonstrated that the coarsening of the precipitates can be accelerated under higher stress. The comparison of Figure 6b,e shows that the average diameter of the η -precipitate after stress relaxation aging of 6% pre-strain is about 20 nm.…”

“…σ is the initial stress. Equation (14) indicates that the decrease of stress relaxation rate is due to the slowdown of strain rate. E(T) represents the change of Young's modulus with temperatures within experimental temperature.…”

“…The particle swarm algorithm was used for fitting the SRA curves. To prevent the program from producing no physical meaning constants and obtain more accurate material constants of Equation (14)(15)(16)(17)(18)(19), the stress relaxation curves under the four experimental conditions (i.e., 0% + 300 MPa + 140 • C, 0% + 350 MPa + 140 • C, 0% + 300 MPa + 170 • C, 6% + 300 MPa + 140 • C) were fitted by manually modifying the range of material constants, as shown in Figure 11a. Standard deviation of the experimental data and the fitted data is used as a criterion for fitting accuracy.…”

“…Zhang et al [12] and Ma et al [13] extended the equation to a wider stress and temperature range and characterized the microscopic factors (precipitate size, volume fraction and aspect ratio) in more detail. Zheng et al [14] established a deformation constitution model of the stress relaxation. Although the forms of the characteristic equation in their models of precipitates were different, the precipitated strengthening effect is introduced into the model by contributing to the yield strength of the material.…”

Effect of Pre-Stretching on Microstructures and Mechanical Behaviors of Creep-Aged 7055 Al Alloy and Its Constitutive Modeling

“…Due to too many material constants needed to compute in the current constitutive equation, it is difficult to properly fit creep curves using the gradient-based optimization algorithm. With the above creep experiment data for studied 7055-T6 alloy, an advanced algorithm [27], i.e., Genetic Algorithm Optimization Toolbox (GAOT), is employed on MATLAB (Matlab2016a, MathWorks, Inc., Natick, MA, USA) platform to obtain exact constants that can describe the feature of creep and effect of pre-stretching on material, as listed in Table 2. Figure 9 shows the results between fitting predicted curves and experiment data.…”