EXPERIMENTAL AND COMPUTATIONAL INVESTIGATION OF THE CYCLIC MECHANICAL BEHAVIOR AND DAMAGE EVOLUTION OF DISTALOY AE + 0.5% C

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1 Powder Metallurgy Progress, Vol.11 (2011), No EXPERIMENTAL AND COMPUTATIONAL INVESTIGATION OF THE CYCLIC MECHANICAL BEHAVIOR AND DAMAGE EVOLUTION OF DISTALOY AE + 0.5% C M. Schneider, H. Yuan Abstract The present paper deals with the cyclic hardening plasticity o Distaloy AE. Two classical plasticity models, kinematic and isotropic hardening plasticity, are used to approximate hysteresis loops which are taken rom low cycle atigue experiments. It can be conirmed that the superposition o both models shows the best results. Cyclic stress-strain curves and corresponding atigue strain-lie curves or dierent strain-ratios are identiied. Following the loading eects, the microstructures were analyzed. The changes o the micro- and macro-hardness, plain porosity and Young s modulus can be considered as damage evolution. The experiments show that there is a correlation between the elastic domain and the micro-hardness. A drop o the micro- and macro-hardness cannot be observed. Keywords: Distaloy AE, isotropic hardening, kinematic hardening, low cycle atigue INTRODUCTION In [1] a successul application o the combined hardening model was presented. The combination o the kinematic hardening model and the isotropic hardening model were applied to ASC with a density o ρ = 7.2 g/cm³ and ρ = 6.8 g/cm³. Two strain-ratios, R(ε) = -1 and R(ε) = 0, were investigated. With that model dierent mechanical eects can be simulated. The kinematic hardening model allows the description o the Bauschinger eect and the mean stress relaxation (translation o the yield surace). With the isotropic hardening model it is possible to describe ratcheting strains and the so-called strain hardening (expansion o the yield surace) [2,3]. ASC shows a strong hardening in the cyclic stress-strain curves above the yield point elongation. For lower strains the material is sotened. The Manson-Coin plots reveal no eects o mean strain [1]. It is o interest to compare the results taken rom ASC with the mechanical behavior o a high strength material like Distaloy AE, which has a wider application range in industry. The present paper deals with the cyclic properties o Distaloy AE, experimental and computational results are compared. EXPERIMENTAL WORK Testing conditions Tensile specimens with a cross section o A = 48 mm² (width w = 6 mm) were made rom Distaloy AE + 0.5% C with a density o ρ = 7.2 g/cm³. The specimens were Markus Schneider, Huang Yuan, University o Wuppertal, Department o Mechanical Engineering, Wuppertal, Germany Markus Schneider, GKN Sinter Metals Engineering GmbH, Radevormwald, Germany

2 Powder Metallurgy Progress, Vol.11 (2011), No sintered at ϑ = 1120 C or t = 20 min in a belt urnace. The atmosphere consisted o 95% N 2 + 5% H 2. The experiments or the cyclic stress-strain curves and the additional strainlie curves (Manson-Coin) were ran under strain-controlled loading conditions on a conventional mechanical testing machine with a requency o = 0.1 Hz. The low testing requency is based on the machine design. Eects o dierent requencies were not taken into consideration. Cyclic properties o Distaloy AE + 0.5% C The cyclic stress-strain curve is constructed with stable stress amplitudes σ a = Δσ/2. It is assumed that hysteresis loops stabilize at N /2, where N denotes the cycles to ailure. The cyclic values are itted with the Ramberg-Osgood relation: 1 n σa σa εa = + E K (1) where ε a = Δε/2 denotes the strain amplitude, E is Young s modulus, K is the strength coeicient and n is the strain hardening exponent. The Manson-Coin relationship is: σ b ε ( ) ( ) c a = 2N + ε 2N (2) E where σ denotes the atigue strength coeicient, ε is the atigue ductility coeicient, b is the atigue strength exponent and c is the atigue ductility exponent. The parameters are related with the Ramberg-Osgood parameters as ollows: σ K = (3) ( ε ) n b n = (4) c Distaloy AE + 0.5% C shows a hardened behaviour above ε a = 0.25%. The corresponding strain-lie curves display an eect o the strain-ratio. The strain-ration o R(ε) = -1 leads to a higher N. The itted parameters are given in Table 1. Tab.1. Ramberg-Osgood and Manson-Coin parameters o Distaloy AE + 0.5% C. R(ε) E [GPa] ν K [MPa] n ε c

3 Powder Metallurgy Progress, Vol.11 (2011), No (a) (b) Fig.1. Monotonic and cyclic stress-strain curves o Distaloy AE + 0.5% C with ρ=7.2 g/cm³ (a) and the additional strain-lie curves (b). COMPUTATIONAL WORK Parameter identiication For the description o the combined hardening behavior two evolution laws are needed. The kinematic hardening model needs the evolution o backstress α over the plastic strain range Δε p as internal variable. For that model it is assumed that hysteresis loops stabilize ater the irst cycle. The isotropic hardening model needs the evolution o the elastic domain k over the accumulated plastic strain p = 2NΔε p. It is common to use itting unctions that show a saturation behavior. The evolution o backstress α is expressed with:

4 Powder Metallurgy Progress, Vol.11 (2011), No Δσ C γ Δεp α = k = tanh (5) 2 γ 2 There are three parameters to identiy: The elastic domain 2k, the asymptotic value o saturation C/γ and a coeicient γ which describes the slope. To improve the elastic domain 2k due to strain hardening it is necessary to vary k with p: k = k0 + Q (1 exp( B p)) (6) The initial elastic domain ater the irst cycle is 2k 0. Where the asymptotic value is k 0 +Q, B is the rate o stabilization. All itting parameters were estimated with experiments using a strain-ratio o R(ε) = -1. The hardening parameters are given in Table 2. (a) (b) Fig.2. Identiication o the nonlinear kinematic hardening parameters o Distaloy AE + 0.5% C with ρ = 7.2 g/cm³ (a) and the corresponding isotropic hardening parameters (b).

5 Powder Metallurgy Progress, Vol.11 (2011), No Tab.2. Combined hardening parameters o Distaloy AE + 0.5% C. k 0 [MPa] C [MPa] γ Q [MPa] B Comparison o experimental and computational results The computations were perormed with ABAQUS implicit. Fig.3. Experimental observations or two dierent strain amplitudes ε a = 0.6 % and ε a = 1 %, two dierent strain-ratios R(ε) = -1 and R(ε) = 0 and corresponding results o the computations. Veriication experiments with notched tensile bars The agreement between the experiments and the computations under straincontrolled conditions are very good. To veriy the parameters stress-controlled tests were perormed with notched tensile bars. The specimens were modiied with a drill-hole (d = 2.1 mm), located in the centre o the specimen. The theoretical stress concentration actor is K t = 2.4. The specimens were loaded with a orce amplitude o F a = N at a stressratio o R(σ) = 0.

6 Powder Metallurgy Progress, Vol.11 (2011), No (a) Fig.4. Experiment (a) and computation (b). (b) DAMAGE EVOLUTION Structural changes o the microstructure which are related with pore or microcrack growth, nucleation and coalescence are called damage [4]. The state o damage can be described with an internal variable D [5]. A relationship between that variable and the plastic strain ε p (monotonic loading case) or the accumulated plastic strain p (cyclic loading case) is called evolution o damage [5]. Lemaitre and Desmorat have deined some eects which can be used or inverse methods to evaluate the evolution o damage. They propose a decrease o Young s modulus E and o the hardness H. A decrease o the hardness can only be observed or an elastic-perect plastic material without hardening, otherwise both eects interact. To improve that inverse technique Tasan, Hoenagels and Geers propose a heat treatment which consists mainly o a recrystallization process to generate a strain ree microstructure without hardening [6,7]. This idea was applied to Distaloy AE. A recrystallization temperature o ϑ = 610 C and an exposure time o t = 30 min (slow cooling inside the urnace) were selected. The hardness was measured at two dierent positions: close to the racture surace (racture) and with a distance o 20 mm (matrix). Two dierent orces were realized: HV 0.1 (applied on pearlite) and HV 5 (applied on the whole material). The HV 0.1 hardness shows an increasing saturation behavior. Hence, the modiied isotropic hardening unction, equation 6, was applied to describe the HV 0.1 hardness. The rate B is assumed to be constant: HV = HV + Q (1 exp( B p)) (7) 0 HV Tab.3. Hardness HV 0.1 values o Distaloy AE + 0.5% C (not heat-treated, matrix). HV 0 [MPa] Q HV [MPa] B For p = 0: HV HV = 0 = 0.77 (8) k k 0 For p :

7 Powder Metallurgy Progress, Vol.11 (2011), No HV HV0 + QHV = = 0.76 (9) k k + Q 0 (a) (b) Fig.5. Micro-hardness HV 0.1 as a unction o p (a) and macro-hardness HV 5 (b).

8 Powder Metallurgy Progress, Vol.11 (2011), No CONCLUSIONS Distaloy AE + 0.5% shows a cyclically hardened behavior above a strain amplitude o ε a = 0.25%. The cyclic stress-strain curves or two dierent strain-ratios are congruent. Dierent rom ASC , the eect o mean strain is recognizable in the Manson-Coin plot. Both the Ramberg-Osgood and the Manson-Coin relationships give a proper approximation o material s response. The computations using the combined hardening model show a very good agreement with experimental observations. The model parameters are valid or dierent strain-ratios. Even stress-controlled experiments with notched specimen (triaxial stress state) show acceptable results. Ratcheting strains can be predicted. The Vickers hardness HV 0.1 can be related to the elastic domain 2k. While the HV 0.1 hardness increases with the accumulated plastic strain, the HV 5 hardness shows a small drop. The HV 0.1 hardness close to the racture surace is somewhat higher than o the matrix material. This can be related to higher local strains. Ater a recrystallization heat treatment the HV 0.1 hardness shows no hardening. The HV 0.1 hardness is more or less constant. Both recrystallized and not heat-treated specimens reach or p = 0 (no deormation) nearly the same HV 0.1 hardness. This reers to a successul heat treatment. Aected by the porosity, the HV 5 hardness is in general lower than the HV 0.1 hardness, but a signiicant drop in the HV 5 hardness, which can be related to damage (sotening due to micro-cracks), is not observable. REFERENCES [1] Schneider, M., Yuan. H.: Experimental and computational investigation o cyclic mechanical behavior o sintered iron, submitted to Computational Materials Science, 2010 [2] Simo, JC.: Computational Inelasticity. 2nd ed. Berlin : Springer Verlag, 2000 [3] Lemaitre, J., Chaboche, JL.: Mechanics o solid materials. 1st English ed. Cambridge : Cambridge University Press, 1990 [4] Gross, D., Seelig, T.: Bruchmechanik. 4 th ed. Berlin : Springer Verlag, 2007 [5] Lemaitre, J., Desmorat, R.: Engineering Damage Mechanics. Berlin : Springer Verlag, 2005 [6] Tasan, CC., Hoenagels, JPM., Geers, MGD.: Scripta materialia, vol. 63, 2010, p. 316 [7] Tasan, CC., Hoenagels, JPM., Geers, MGD.: Acta materialia, vol. 57, 2009, p. 4957