2 | TEST MATERIAL AND CONSTITUTIVE RELATION
The AISI 5140 steel was obtained
from a large reciprocating compressor crankshaft with a diameter of 200
mm. The crankshaft was first forged with a temperature between 850 and
1150 oC and air cooled to room temperature. Then it
underwent the heat treatment process with a quenching temperature 850 ofoC, a tempering temperature of 590oC and cooling with oil. The chemical compositions of
the steel were measured and are listed in Table 1. The microstructure of
the AISI 5140 steel was mainly composed of fine pearlites, tempered
sorbites and proeutectoid ferrites around prior austenite grain
boundaries, and the grain size was about 20-30 μm, as shown in Figure 1.
Quasi-static and dynamic mechanical properties of the AISI 5140 steel
were measured using the electro-hydraulic servo testing machine and HPB.
True stress-strain curves in the plastic stage are presented in Figure
2, and yield strengths of the steel at different strain rates are shown
in Figure 3. The dynamic yield strengths are 847.7 MPa and 892.0 MPa at
the strain rates 3057 s-1 and 4700
s-1 respectively, which increased by 37.8% and 45.0%
compared to the quasi-static value 615.2 MPa. The dynamic yield strength\(\sigma_{\text{yd}}\) can be expressed with the quasi-static one\(\sigma_{\text{ys}}\) and the strain rate \(\dot{\varepsilon}\) in
Cowper-Symons form:
\(\sigma_{\text{yd}}=\sigma_{\text{ys}}\left(1+\frac{{\dot{\varepsilon}}_{\text{eq}}}{C}\right)^{\frac{1}{p}}\)(1)
where \(C\)= 257.8, and \(p\) = 8.0 are material constants related to
strain-rate hardening.
As shown in Figure 2, the AISI 5140 steel is sensitive to strain rate
and the flow stress increases with the increasing strain. Therefore, the
dynamic constitutive relation of the steel is expressed with the strain
hardening term and the strain-rate hardening term
\(\sigma_{\text{eq}}={\left(A_{1}+A_{2}\varepsilon_{\text{eq}}^{n}\right)\left(1+\frac{{\dot{\varepsilon}}_{\text{eq}}}{C}\right)}^{\frac{1}{p}}\)(2)
where \(\sigma_{\text{eq}}\) is equivalent stress,\(\varepsilon_{\text{eq}}\) is equivalent strain, and\({\dot{\varepsilon}}_{\text{eq}}\) is equivalent strain rate. \(A_{1}\)= 615.2 MPa, \(A_{2}\) = 863.7 MPa, and \(n\) = 0.45 are material
constants related to strain hardening. It is clear from Figures 2 and 3
that the test data of the stress-strain relation and the yield
strength-strain rate relation can be well explained by Equations (1) and
(2).