Abstract
It has been known for a long time that spalling (dynamic tensile failure) is a rate dependent process. Spall strength of metals is determined from the pullback velocity of the free surface velocity history in planar impact spalling tests. Conducting these tests for different volume strain rates in the tension zone, it was established that spall strength increases with strain-rate according to a power law: Strength spall = A ∗ (rate) m , where the power m is a small number compared to unity. Nevertheless, standard spall models in commercial and propriety hydrocodes use constant spall strength, and are not able to predict the rate dependence. We propose here a rate dependent spalling model which is based on the overstress concept. In a constant spall strength model, when the negative pressure reaches the negative spall-strength value, pressure is put to zero within a single time step. In our rate dependent model we allow the negative pressure to go above the current negative spall-strength according to specified rate coefficients (calibrated from tests), while the negative pressure is decreased proportional to the amount of overstress above the current negative strength value. We calibrate our rate coefficients according to experimental data for a Stainless Steel and demonstrate how the model works using a 1D hydrocode for planar impacts with different strain rates in the tension zone.
Highlights
It has been known for a long time that spalling is a rate dependent process [1].Spall strength of metals is determined from the pull back velocity of the free surface velocity history in planar impact spalling tests
Conducting these tests for different volume strain rates in the tension zone up to a strain rate of 107 1/sec, it was established that spall strength increases with strain rate according to a power law: Pk = A(εV )m εV
Spalling tests show that spall strength, as inferred from pullback velocity signals, is rate dependent
Summary
It has been known for a long time that spalling (dynamic tensile failure) is a rate dependent process [1]. Spall strength of metals is determined from the pull back velocity of the free surface velocity history in planar impact spalling tests Conducting these tests for different volume strain rates in the tension zone up to a strain rate of 107 1/sec, it was established that spall strength increases with strain rate according to a power law: Pk = A(εV )m εV. Accounting for strain rate dependence of spall strength has great importance when extrapolating experimental plate impact test results to practical problems involving various loading histories such as cases involving an explosive loading. The negative pressure relaxes back towards the quasi-static strength at a rate that increases with the amount of overstress. This rate of relaxation is the source of the rate dependence observed in spall tests. From the results we are able to calibrate the two parameters in the negative pressure relaxation equation
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