Residual life prediction for healing fatigue damaged copper film by laser shock peening

Abstract

A B S T R A C T A healing method for fatigue damage was studied by laser shock peening (LSP) with excimer laser for polycrystalline copper film. It is found that work hardening due to LSP could be responsible for the improvement of residual fatigue lives for the damaged and undamaged specimens by LSP, and the hardening degree for the damaged specimen by LSP is obviously higher than that for the undamaged specimen by LSP. In this paper, two basic mechanisms were identified. One is the dissipated energy enhancement mechanism, which improves the fatigue life caused by laser shock stress, and the other is the healing mechanism, which leads to a further improvement. Based on the two mechanisms, a residual fatigue life prediction method is proposed by the view of energy consumption before and after LSP. The predicted lives by the proposed method agree well with the experimental results.Keywords laser shock peening; work hardening; dissipated energy enhancement mechanism; healing mechanism; life prediction.coefficient for the original specimen by LSP k D ¼ hardening coefficient for the damaged specimen by LSP m ¼ modified exponent of hardening degree N 0 ¼ fatigue life for original specimen N D ¼ consumed life of the damaged specimen N DEEM ¼ improved fatigue life caused by the extra plastic strain energy for the original specimen by LSP N D DEEM ¼ improved fatigue life caused by the extra plastic strain energy for the damaged specimen by LSP N LSP D¼0 ¼ fatigue life for the original specimen by LSP N HM ¼ pure healing life caused by HM N r ¼ residual life of the damaged specimen by LSP n′ ¼ cyclic hardening exponent of the material ΔW p0 ¼ plastic strain energy for the original specimen without LSP ΔW LSP;D p ¼ plastic strain energy for the damaged specimen with LSP ΔW LSP;D¼0 p ¼ plastic strain energy for the original specimen with LSP Δσ ¼ stress range Δε p ¼ plastic strain range Δε p0 ¼ plastic strain range of specimen without LSP Δε LSP p ¼ plastic strain range of specimen with LSP Δε LSP;D¼0 p ¼ plastic strain range of the original specimen with LSP Δε LSP;D p ¼ plastic strain range for the damaged specimen by LSP

A nonlinear fatigue damage‐healing model for copper film by LSP

“…The nonlinear fatigue damage‐healing model was verified by the experimental data in Ref [], as listed in Table . Two conditions were contained in Table .…”

“…Therefore, the damage variable D can be defined as the ratio of the damage energy dissipation with the fatigue ductility: where W D is the consumed fatigue ductility for the damaged specimen, which is the sum of the consumed plastic strain energy per cycle, and W f is the fatigue ductility for the original specimen, which is the total plastic strain energy during the fatigue process. The fatigue ductility for material can also reflect the mechanical performance, which also can describe the fatigue strength of micro‐structural component, such as Kanda et al Liu et al found that the variation of the fatigue ductility, the sum of plastic strain energy per cycle, can be used to describe the change of fatigue life before and after LSP. According to the Ref.…”

“…can be expressed as where Δ W H and Δ W f can be calculated by where ε Ha p and ε fa p are the plastic strain amplitudes for the damaged specimen after LSP and the original specimen, respectively; n H ′ and n f ′ are the cyclic hardening exponents of the damaged specimen after LSP and the original specimen, respectively; and σ Ha and σ fa are the stress amplitudes of the damaged specimen after LSP and the original specimen, respectively. Because the cyclic strain hardening exponent of the material and the applied stress before and after LSP is changeless, according to Eqs and , Eq. can be written by …”

“…The fatigue life of pure enhancement for the damaged specimen by LSP can be calculated by where is the fatigue life for the undamaged specimen after LSP and ε Sap is the plastic strain amplitude for the undamaged specimen after LSP. The proposed nonlinear fatigue damage‐healing model under the constant amplitude loading condition in this investigation can be expressed as …”

“…The plastic strain amplitude can be obtained by subtracting the elastic strain amplitude from the total strain amplitude, in which the total strain amplitude can be measured easily in engineering application. The fatigue lives for the undamaged specimens by LSP healing treatment are listed in Table . The parameter α is calculated by Eq.…”