PSI - Issue 28

NikolayA. Makhutov et al. / Procedia Structural Integrity 28 (2020) 1347–1359 N.Makhutov, D.Reznikov/ Structural Integrity Procedia 00 (2019) 000–000

1356 10

where 0 f е is the initial plasticity (in normalized coordinates). When the influence of strain rate ( f 2 ) and temperature ( f 3 ) factors according to expressions (4) and (5) were assessed the moment of the initiation of a crack in the notch zone under low-temperature high-speed loading (Fig. 2c) can be predicted using the equations (6) and (31). Then the value of the ultimate impact load P can be estimated. 5. Design example The analysis of high-speed low-temperature deformation a Charpy specimen (Fig. 4a) was considered as a design and experimental example. The specimen was made of steel St3 with the following mechanical properties yield strength σ y =252 MPa, ultimate strength σ u =507 MPa, fracture stress S f =1070MPa, critical value of the relative narrowing of the cross section ψ f0 = 54.3%. They determine the hardening index m 0 . The geometric dimensions of the specimen: b = 10 mm , h =8 mm, l =2 mm, ϱ = 0.1 mm. The magnitude of the impact load P varied in experiment and design. The results of an experiment study of impact loading of Charpy specimen (Bondarovich, Zlochevsky, Makhutov, 1980) were used to estimate the strain rate (Fig. 4). The rate of the specimen loading was about 11,6ꞏ10 4 N/s, and the strain rate е  was about 1,8ꞏ10 1 1/s.

Fig. 4. Data from an experimental study (Bondarovich, Zlochevsky, Makhutov, 1980) Oscillogram P-τ recorded by a dynamometer of the hammer

The factor I c that characterizes the increase in the first principal stress σ 1 (Fig. 5a) at which plastic strains begin in the notch zone is determined with accounting for the change in the stress state over the cross section of the specimen in the notch zone (Fig. 5b). Obviously σ 3 =0, and σ 2c in the notch zone varies over the cross section from 0 on the surface of the specimen to μσ1c in its central part. We assume that the change in σ 2c over the thickness of specimen b can be approximated by a piecewise linear function (Fig.5b) with the thickness of the transition zone δ=0.2 b . Then, the average value of I c over the thickness of the specimen can be determined by integration:

b

1 b



 2

.



2 ( ) 1 1,11 x dx  

2  2 / (1 ( ) x 

c I





2 

0



      

0

;

x

for

x  



 

(32)

( ) x

;

for

x b   









2

( (    x b  

))

.

for b

x b



   



Then using the equation (23) it is possible to estimate the yield strength σ y for considered case of low-temperature dynamic loading inside and outside the notch zone.