Template For The Preparation Of Papers For On-Line Publishing In JSME

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1 A Cnstitutive Equatin f Strain Rate Deendency fr Varius Cyclic Ladings Akihir HOJO, Jianxun SHEN, Akiyshi CHATANI and Hirshi TACHIYA * * * * Det. f Mechanical Systems Engineering, Kanazawa University, Kdatsun, -4-, Kanazawa, Ishikawa, , Jaan The resent aer rsed a new cnstitutive equatin deendent n the strain rate by intrducing the inner-state variables. Using these variables, we can describe the behavir f materials, withut distinctin between lading and unlading, and elastic and lastic state. The histry effects f cyclic hardening and sftening are als incrrated int the equatin. Cyclic lading exeriments with eight tyical strain arts were cnducted using SUS34 stainless steel. The resent cnstitutive equatin was alied t the measured stress-strain relatins. As a result, it agreed well with the exerimental values fr btaining stable cyclic stress-strain relatinshi under rrtinal and nnrrtinal ladings. And the exerimental cnstants included in the equatin were fund t be valid fr ractical use. Key Wrds : Cnstitutive equatin, Cmbined stress, Inelasticity, Stress relaxatin, Strain rate, Cyclic lad, Inner-state variables, Nnrrtinal. SUS34 () (5). (3) E e ν e σ& = & ε + δ & εkk () + ν ν (4) e & ε = & ε & ε RambergOsgd e ε ε ε E ν δ ()

2 Perzyna (5) 3 g( O) & ε = O () K O kk 3 () O = s α, s = σ δ σ, O= OO 3 α s O O α α& α K α K K= K ( α ) sat α& = K & ε (3) Re lad ing Un lad ing 3 α = αα (4) α α max (3) K () g () Fig. The lading cnditin K sat ( α ) σ = σ, α = α (5) () O = σ α (6) OA A σ α α α max α& α & ε = g( σ α) A α < α max α& α /sec α max α (6) g ( x) = ex( C + x / C ) (7) g () = K C K= K sat( α max) K = K sat() C A" A' A" A' K= Kβ + K β (),(3) g () A" A A" A K= Kβ + K β β ( x), x (3) α = α max α K= Kβ ( ξ) + K{ β( ξ )} (8)

3 BC s + s cs θ scsθ ξ = = (9) CC' s + s csθ s = α / α, K = K (), K = K ( α ) max sat sat max (CDV3C) α & (NECPC98) α csθ = () αα & α & α () csθ α& α csθ = csθ = () αα θ cs & = () α α & α & α.sec 94(N) α& 96(N m) ε& O α, O (8) K (CSK543AP-TG) 5: 3 5 : (N m) W 4 3 (/ sec) (PMC- M798BPC khz ) PC-98 I/O ε, γ σ, τ : Aut Grah : Crss Head : Trsinal Device : Secimen : Lad Cell : Steing Mtr Fig.Blck diagram f multiaxial cyclic lading test (a). Exerimental strain ath.(b). Ideal strain ath Fig.Exeriment n case 3 (Case ) 3 ±.5%

4 (a) (/ sec). 5% 35 8 C = 9, C =.35Ma Ksat ( x) = E{ κ + κ ex( x/ κ3) } () β β ( x) = x (3) κ =., κ =.9, κ3 = 43Ma, β =.65 E = 8Ga, ν =.33, C Fig. Shae and dimensins f the secimen ( (/ sec) ) ()(3) 4 Runge-Kutta (7) K sat 6 ε γ / 3 ϕ= tan ( γ/ 3 ε) ϕ ( ) ( ) ϕ ()(3) (a) Case (b) Case (c) Case 3 (d) Case 4 (e) Case 5 (f) Case 6 (g) Case 7 (h) Case 8 Fig.Ideal strain ath ()θ 8 θ 9 θ C

5 φ3 { ( )} & = φsinθ + lg + φε ε (4) C θ 9 θ 789 φ = 5Ma, φ = 45, φ3 = 3.3 (Case )(Case 3) C& = (Case 4) (a) (c) ε (b) θ 9 C (d) ε θ 9 C θ (4) σ σ τ σ (a). tan ( γ / 3 ε) = σ τ σ τ (b). tan ( γ / 3 ε) = 3 σ τ τ (c). tan ( γ / 3 ε) = 6 τ σ τ (a). Stress-strain (Exeriment). (b). Stress-strain (Calculated) (d). tan ( γ / 3 ε) = 9 Fig.Results fr case (c). Stress ath (Exeriment) (d). Stress ath (Calculated). Fig. 8 Results fr case 3 - (a). Stress-strain (Exeriment). (b). Stress-strain (Calculated). - σ τ σ τ (c). Stress ath (Exeriment) (d). Stress ath (Calculated). Fig. 7 Results fr case σ τ

6 C θ (a). Stress-strain (Exeriment). (b). Stress-strain (Calculated). - σ τ σ τ σ τ (c). Stress ath (Exeriment) (d). Stress ath (Calculated). (a). Stress-strain (Exeriment).(b). Stress-strain (Calculated). Fig. Results fr case 6. σ τ (c). Stress ath (Exeriment) (d). Stress ath (Calculated). Fig. 9 Results fr case 4 - σ τ σ τ (a). Stress-strain (Exeriment).(b). Stress-strain (Calculated) (c). Stress ath (Exeriment) (d). Stress ath (Calculated). Fig. Results fr case 5 - σ τ σ τ (a). Stress-strain (Exeriment). (b). Stress-strain (Calculated) (c). Stress ath (Exeriment) (d). Stress ath (Calculated). Fig. Results fr case 7 4 (Case) θ

7 SUS34 (a). Stress-strain (Exeriment). (b). Stress-strain (Calculated). ) ) (c). Stress ath (Exeriment) (d). Stress ath (Calculated). Fig. 3 Results fr case 8 3) 4) [ ] [ ] T. Ith, X. Chen, T. Nakagawa and M. Sakane, Trans. ASME, J. Eng. Mater. Technl, (),. J. H. Fan, X. H. Peng, Trans. ASME, J. Eng. Mater. Technl, 3(99), A(99)767. σ τ σ τ Case - Case - Case 3 Case 3 Case 5 Case 5 Case 7 Case 7 Fig. 4 Cmarisn f cyclic hardening 5653A(99)536. P. Perzyna, Quart. Al. Math, (963), (6)4. 3.