PSI - Issue 61

Necdet Ali Özdür et al. / Procedia Structural Integrity 61 (2024) 277–284 N.A. O¨ zdu¨r et al. / Structural Integrity Procedia 00 (2024) 000–000

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5

• No external heat supply • Small deformations • Negligible thermal couplings of internal variables • Thermoelastic e ff ects limited to isotropic heat expansion • 0D thermal di ff usion

which reduces the local thermal equilibrium equation given in Eq. 5 to the following form ρ 0 C ˙ T + ρ 0 CT τ eq = βσ : ˙ ε p − α T tr( ˙ σ )

(6)

W s + W l = β W a + W is , (7) where W s , W l , W a , and W is denote the energetic contributions related to thermal storage, convectively lost energy, applied plastic work, and thermoelastic e ff ects, respectively. τ eq that appears in the 0D thermal heat loss term, W l , is a measure of characteristic time that describes how quickly the material loses heat to its surroundings both conductively and convectively; it is the only remaining unknown term in Eq. 6 except for β . The definition of τ eq in 0D thermal di ff usion is originally derived by Doudard et al. (2010) as follows: 1 τ eq = 2 h 1 ( e + l ) el + 2 h 2 L (8) Here, e , l , and L correspond to the specimen dimensions of thickness, width, and length; while h 1 and h 2 denote the air-film coe ffi cient and the apparent film coe ffi cient between the grips and the specimen. The aim of the polycrystal plasticity simulation is only to produce a statistical representation of the thermomechan ical response of a large aggregate in the average sense. The simulation is therefore simplistic and is not expected to capture detailed non-local and inter-granular mechanical interactions. To this end, a Taylor-type simulation domain consisting of 172 grains, oriented such that it resembles the rolling texture of the sample is generated, using Neper by Quey et al. (2011). The texture used for the simulation can be seen in Fig. 5(c). The domain is compressed along its ‘rolling direction’ with a strain rate of 0.2% s − 1 for 16 seconds such that it reaches to 3.2% strain at the end of the simulation, in line with the experiment. For the case study, the visco-plastic material model by Chang and Kochmann (2015) is implemented, which is already cast in variational form. Briefly, the model uses a pseudo-slip homogenization approach for tensile twins, 2.5. Crystal Plasticity Simulation

Fig. 3. (a) Stress (blue) and change in temperature (red) with respect to strain. (b) The decay of average surface temperature measured after the end of the experiment. Blue line is an exponential fit to the temperature data. Above the figure is the functional form used in data fitting.