ScienceDirect Simulation of thermomechanical ...

Available online at www.sciencedirect.com

ScienceDirect Procedia Engineering 74 (2014) 352 – 355

XVII International Colloquium on Mechanical Fatigue of Metals (ICMFM17)

Simulation of thermomechanical fatigue of structured materials Yury Temisa,b, Alexander Fakeevb a

Bauman Moscow State Technical University (BMSTU) 5, 2nd Baumanskaya St., Moscow, Russia b Central Institute of Aviation Motors (CIAM) 2, Aviamotornaya St., Moscow, Russia

Abstract Technology of low-cycle fatigue simulation under nonisothermal loading was developed. It is based on the two models: threeparametric model of cyclic stress-strain curve which determines set of thermomechanical surfaces of plastic strain and damage model. Based on experimental results under isothermal cyclic loading thermomechanical surfaces of cyclic loading were created. Parameters of cyclic stress- strain curves were determined by the processing of the experimental data by the optimization techniques. Parameters of damage model were determined by the least squares method. A program for simulation of specimen tests under nonisothermal cyclic loading was developed for the verification of the proposed models under various types of cyclic loading. Influence of creep and creep rupture strength was taken into account in the simulation of nonisothermal cyclic stressstrain curves and low cycle fatigue respectively. Mathematical simulation of the various experiments in literature of thermomechanical fatigue was carried out for the performing of efficiency of the proposed models and programs. © 2014 The Authors. by Elsevier Ltd. under CC BY-NC-ND license. © Published by Published Elsevier Ltd. Open access Selection and Politecnico di di Milano, Dipartimento di Meccanica. Selection and peer-review peer-reviewunder underresponsibility responsibilityofofthethe Politecnico Milano, Dipartimento di Meccanica Keywords: Plasticity, cyclic loading, thermomechanical fatigue.

1. Introduction The technology of simulation of low cycle fatigue of specimens and parts was originally developed under isothermal cyclic loading conditions [1,2]. Generalization of this technology of the simulation under nonisothermal cyclic loading was proposed in works [3,4] . For the description of the cyclic stress-strain curves the hypothesis about existence of the set of thermomechanical surfaces was used. Information about results of basic tests of specimens under cyclic isothermal loading was used for the creating set of thermomechanical surfaces. For the life assessment the hypothesis about existing the ultimate value of the cumulative plastic strain under cyclic loading was used. In this paper results of the verification of the material and damage models obtained by the processing of experimental data [5-8] under nonisothermal cyclic loading were provided.

1877-7058 © 2014 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. Selection and peer-review under responsibility of the Politecnico di Milano, Dipartimento di Meccanica doi:10.1016/j.proeng.2014.06.278

353

Yury Temis and Alexander Fakeev / Procedia Engineering 74 (2014) 352 – 355

2. Material models Three parametric model which is used to simulation elasto-plastic stress-strain response makes it possible to describe dependence of Bauschinger effect, nonlinear part of stress-strain curve and Young's modulus versus total cumulative plastic strain under nonisothermal cyclic loading [3,4]. This model based on consideration of the thermomechanical surface under cyclic or complex loading. Part of this thermomechanical surface which is located between isothermal cyclic stress-strain curves at temperatures T1, T2 and at current value of cumulative plastic strain is described by relations: *

*

σ = F (ε p , T ), F = (1 − λ ) f1 + λ f 2 , λ =

T − T1

(1)

T2 − T1

* Ê E (Ti ) ⋅ d ( χ , Ti ) ⋅ ε , ε * ≤ ε S* Í * * fi = Ë Ç Ã Ô ε − εS * * * χ ε χ χ ε E T ⋅ d T ⋅ + d T ⋅ b T ⋅ f + ( ) ( , ) ( , ) ( , ) i s i i Í i È Ä S b ( χ , T ) , Ti Õ − σ S (Ti ) Ù , ε > ε S Ì É Å Ö Ú i

(2)

i = 1, 2, σ s ( T ) = a ( χ , T )σ s (T ), ε s = a ( χ , T ) / d ( χ , T ) ε s *

*

Nomenclature correlates with works [1-4]. In [1,2] based on experimental results it was determined that at room temperature number of halfcycles to failure for several structural materials under various loading programs (soft loading, hard loading, random loading) nf and damage D depends on ultimate value max by next relation: γ

n f = ( χ max / δ ) , D = χ / χ max

(3)

where δ and γ is material constants. where – cumulative plastic strain on the current step, max defined by the relation (3) limit value of cumulative plastic strain The beginning of the LCF crack grown in the specimen or the structure corresponds to value of damage level which equals unity. It can be possible to show that the Coffin-Manson relation [5] is the special case of the relation (3) under the constant value of the plastic strain on each half cycle. In works [3,4] it was shown that the relation (3) satisfactorily correlates to experimental data under nonisothermal cyclic loading. Based on the experimental data for the determining of the parameters of the model of the nonisothermal cyclic stress-strain curve in the coordinate system ε, σ / E experimental curves of the cyclic loading. E is the averaged Young's modulus at the current temperature. At the k interval for the cumulative plastic strain k and based on current nk experimental points it was determined the parameters ak and bk which was seted at the right bound of the interval by the minimization of the functional:

Â (J nk

J ( ak , bk ) =

1i

( ak ) + J 2 i ( ak , bk )) → min

(4)

i =1

The functional J1 determines the sum of the measures of the errors between experimental and simulated values of the yield stress. The functional J2 determines the sum of the measures of the errors between experimental and simulated values of the extreme points of the half cycles. Under simulation of the cyclic stress strain curves the set of points was determined in the cumulative plastic strain - number of half cycles to failure coordinate system. The limit value of the cumulative plastic strain was

354


calculated. In the logarithmic coordinate system this set of points approximates by the linear relation. Parameters of this relation determines by the least squares method. and correlates with the parameters of the damage model (3) 3. Simulation of cyclic test of smooth specimens under nonisothermal loading The mathematical simulation of the nonisothermal cyclic loading of the smooth specimens from the alloy 2,25CrMoV (experimental data [6,7]) and alloy 1CrMoV (experimental data [8,9]) was provided for the verification of the proposed models. For example the comparison of the results of the simulation and experimental data of the alloy 1CrMoV, which is used in turbomachinery components. Parameters of proposed models for that material was calculated based on experimental data [8,9] of the smooth cylindrical specimens under isothermal cyclic loading The verification of the proposed model was provided by the comparison results of simulation and experimental data at nonisothermal loading by the three types of loading (fig. 1).

a)

b)

c)

Fig. 1:Three cycle types of loading.

In the figures 2, 3, 4 the comparison of the experimental data [8,9] and simulation data at these types of loading is shown. In the figure 2 comparison of cyclic stress strain curves at the 2 cycle (fig. 2a) and at the 30 cycle (fig. 2b) for the loading type 1 is shown. The relations between amplitudes of the stresses and number of cycles for the loading type 1 are performed in the figure 2c. In the figure 3a comparison of cyclic stress strain curves at the 50 cycle for the loading type 2 is shown. The relations between amplitudes of the stresses and number of cycles for the loading type 2 are performed in the figure 3c. The cyclic stress-strain curves at the third cycle type of loading are shown in figure 4a. Lines shows the simulation curves on the 1,2,10,20,50 and 100 half cycles. Points shows the experimental data at the 50 cycle of loading. The relations between amplitudes of the stresses and number of cycles are performed in the figure 4b. The comparison the calculation and experimental numbers of cycles to failure for the all 3 types of loading is shown in the fig. 4c.

a)

b) Fig. 2: Experimental and simulation results of simulation for type 1 of loading.

c)

355


a)

b)

Fig. 3: Experimental and simulation results of simulation for type 2 of loading.

a)

b)

c)

Fig. 4: Experimental and simulation results of simulation for type 3 of loading.

4. Conclusion Presented results indicate a probability application nonisothermal cyclic stress-strain curve model, that generalized on cyclic nonisothermal loading and damage model for calculation stress-strain state and life time prediction. This model may be actual for development of plasticity and damage models for LCF numerical simulation of structures which are working under nonisothermal cyclic high loading.

References [1] Putchkov I. V. Temis Y. M. Dowson A. L. Damri D. Development of a finite element based strain accumulation model for the prediction of fatigue lives in highly stressed Ti components, Int. J. Fatigue, 1995. Vol. 17, No 6, pp.385 – 398. [2] Temis Y.M., Azmetov Kh.Kh., Zuzina V.M. Low-cycle fatigue simulation and life-time prediction of high stressed structures. Solid State Phenomena. Trans Tech Publications, Switzerland, 2009, Vols. 147-149, pp. 333-338. [3] Temis Y. M., Fakeev A. I., Azmetov Kh. Kh. LCF simulation under nonisothermal loading. Proceedings of the 16th International colloquium «Mechanical fatigue of metals» Brno, 24-16 September 2012. pp. 208-215. [4] Temis Y. M., Fakeev A. I., Azmetov Kh. Kh. Numerical simulation of nonisothermal plasticity and thermomechanical fatigue of turbomachinery components. Proceedings of the XII International conference on computuational plasticity. Fundamentals and Applications. Barcelona, Spain, 2013. pp. 1130-1141. [5] Manson S.S. Thermal stresses and low cycle fatigue McGraw-Hill, 1966 404 p. [6] Jaske C. E., Leis B. N. Pugh Monotonic and cyclic stress-strain response of annealed 2,25Cr-1Mo steel. NASA technical report, 1975, 33 p. [7] Manson S. S., Halford G. R., Hirschberg M. H. Creep-fatigue analysis by strain-range partitioning. NASA, 1971. 31 p. [8] Colombo F. Service-like thermomechanical fatigue characteristics of 1CrMoV rotor steel // PhD thesis, Swiss Federal Institute of Technology, 2007. 184 p. [9] Saltsman J. F., Halford G. R. Ability of the total strain version of strainrange partioning to characterize thermomechanical fatigue behavior. NASA, 1994. 24 p.