It is possible to carry out tensile tests at a range of loading strain rates, to characterise material behaviour at the loading rate that will be experienced in service. But it can sometimes be impractical to carry out tensile tests at high loading rates on steel used in existing structures. Therefore, efforts have been underway since the 1970s to predict the effect of loading rate on tensile and toughness properties without having to carry out additional tests.
According to a HSE report from 1999 on the behaviour of carbon steel at high strain rates, both the upper and lower yield stresses and strains increase with increasing strain rates, while the ultimate stress and strain are less sensitive at high strain rates. Also, the strain at initiation of strain hardening was seen as the most sensitive parameter to the effect of strain rates. The effect of strain rate on steels is also dependent on the steel grade, with lower strength steels showing much greater sensitivity to strain rate than very high strength steels. The formulae described below are generally applicable to common structural grade steels.
Based on an extensive test programme on steels of varying strength, Rolfe and Barsom (1977) developed an empirical predictive relationship for structural steel to calculate the influence of the time period and the temperature of a dynamic event on the yield stress:
σyd is the yield stress in MPa at the temperature T (in °K) and the time period t (in seconds) of the event; σys is the static, room temperature yield stress in MPa. This formula would give a rise in yield strength of 65MPa for a isothermal test time of 40ms(corresponding to an average strain rate of about 0.05s-1 for a 50mm gauge length steel specimen at room temperature) and a rise of 140MPa for a isothermal test time of 0.4ms (corresponding to an average strain rate of about 5s-1 for conditions as above), compared to quasi-static test results.
Work by the Steel Structure Committee (SSC) 275 from 1978 on ship steels with yield strengths ranging from 275MPa-690MPa illustrated the effect of strain rate and temperature on yield strength of these steels.
σyd – is the dynamic yield strength
σys – is the static yield strength
ἐo – is the viscosity coefficient taken as 1012/sec
ἐs – is the static strain rate
ἐ – is the dynamic strain rate
V – is the activation volume
K – is the Boltzmann’s constant, 1.38064852 × 10-23 m2 kg s-2 K-1
More recent research work at TWI (Wiesner et al, 2004), published by the HSE has provided an alternative equation for the estimation of dynamic yield strength for ferritic steels at a given temperature and strain rate:
The constants in equation [2] have been estimated by best fitting the equation to test data available in the open literature at the time. The temperature and strain rate ranges covered by the test data are as follows:
Estimation of strain rate is needed in order to use equations [2 and 3], while the loading time period is required in equation [1]. The choice between the equations for estimation of dynamic yield strength will, in practice, depend which input parameter (loading time or strain rate) can be readily estimated, and which is most suitable for the steels to be calculated.
Reference
- S T Rolfe and J M Barson: 'Fracture and Fatigue Control in Structures', Prentice-Hall, New Jersey, 1977, p86.
- C S Wiesner, W Xu, F M Burdekin, W Zhao and Y Tkach: 'The effects of dynamic loading on structural integrity assessments', Research Report, Health and Safety Executive, UK, 2004. ISBN 0 7176 2831 0.
- Health and Safety Executive (1999): “The behaviour of carbon steels at high strain rates and strain limits” Offshore Technology Report – OTO 1999/018, produced by Bomel Limited for HSE, HSE Books.