Stress relaxation in the interface between creep particle and elastic matrix-strengthening mechanism

The effect of a power law creep particle on interface behavior between the particle and elastic matrix is investigated by stress analysis. Using the results obtained through the stress analysis, the forces due to interaction of an applied stress and stress concentration with an edge dislocation are determined. The direct interaction between the edge dislocation and the creeping particle is studied under fully relaxed stress conditions. Through the investigation the following results are derived. Stress relaxation in the interface can be caused by power law creep along or by diffusion, or a combination of both mechanisms. The degree of stress relaxation caused by diffusion can be defined in terms of the relaxation time for both boundary diffusion and volume diffusion. The amount of stress relaxation caused by the power law creep particle is characterized by the quantity ₂ which is a function of Γ₀ = 2(1/√3)^{1 + m} × (σ_∞/2μ)^m(σ₀/σ_∞t^m), where m is strain rate hardening exponent, σ_∞ is applied stress, μ is the shear modulus, σ₀ is the material constant of the power law creep particle, and t is elapsed time. The value ₂ = 1.0 corresponds to the fully relaxed condition and ₂ = −0.6 corresponds to the initial state. The time to reach a fully relaxed condition is very sensitive to the strain rate exponent, with the smaller m values leading to longer times. The stress state of complete relaxation in the elastic matrix is equivalent to the solution of a void in an elastic matrix superposed on the solution of positive surface traction on the void. This result is identical to that obtained by Srolovitz et al. [Acta. Metall.32, 1979 (1984)]. When the stress is completely relaxed in the particle, all stress components (σ_r, σ_θand σ_rθ) are relaxed, while in the matrix relaxations are observed only for σ_rand σ_θ. The critical resolved shear stress and critical stress to climb the dislocation in the neighborhood of the particle exceed the Orowan stress. Also, the particle attracts the dislocation. Therefore the strengthening of a power law creep particle in an elastic matrix is caused by the Orowan mechanism and by attraction of the dislocation.