Issue 27

A. Kostina et alii, Frattura ed Integrità Strutturale, 27 (2014) 28-37 ; DOI: 10.3221/IGF-ESIS.27.04 31 Stored energy calculation Fig. 4 presents field of heat dissipation rate on the small area of specimen surface limited by black rectangle shown in Fig 3b. The small area for calculation was selected due to sample shape changing during deformation process. The field of heat sources is a little bit heterogeneous even during the second part of plastic deformation. Figure 4 : Experimental data of the heat dissipation rate (W/m 3 ) at the beginning and end of interest time range. The integral heat dissipation in zone of interest can be calculated as 22 1 1 ( ) ( , , ) y x x y Q t s x y t dxdy    (2) where 1 2 1 2 , , , x x y y are the rectangular coordinates of the interest zone (Fig. 3b). We suppose that some of the irreversible plastic work contributes to heat generation, while the rest is stored as the energy of crystal defects accompanying plastic deformation, traditionally known as the stored energy of cold work [7,8]. The goal of this work is to calculate value of the stored energy rate. Plastic work spend on deformation of the specimen has to be known for calculation of the energy stored in metals during deformation. We obtained plastic work presented in expression (3) as a function of strain rate V and loading force F(t) . ( ) ( ) p W t F t V  (3) We calculate stored energy of cold work as difference between plastic work spent on deformation and integral heat dissipation ( W p (t)– Q(t) ) [9]. Time dependence of these values is shown in Fig. 5. Ratio ( ) ( ) p Q t W t is usually used for determination of the parameter β characterized extent of material damage [10]. The stored energy ratio can be calculated as follow ( ) ( ) 1 ( ) p p W t Q t W t     (4) In Fig. 6 value of 1– β depending on strain is presented. Value of stored energy decreases in the end of deformation process that means most of plastic work converted into heat and materials prepared to the failure. Red line indicates part from 131.8 sec to 208.9 sec (surface of heat dissipation rate in the beginning and end of this range is presented in Fig.4) described the second part of plastic deformation. This part was chosen for numerical modeling of the plastic deformation process in Armco iron.