I know that at low strain rates the flow stress increases with increase in
strain rate. At higher strain rates it still increases but at a slower rate because of the softening effect due to temperature rise in the material. But what is the philosophy behind this. why dose flow stress increase with increase in strain rate.
A good question!
For metals which harden by the development of dislocations, the increase of the rate of deformation induces a multiplication of the dislocations (increase of their density). This causes the increase of work hardening and consequently the increase of the stress. This is the physical application.
In addition, at high deformation rates, a part of the deformation energy is converted into heat, which softens the material, which creates a competition between work-hardening and thermal softening.
For polymers (amorphous or semi-crystalline), another physical explanation must be given, in relation to their microstructure. For example, for PMMA the strain rate increases the flow stress, but I think it is not due to dislocation development!? See experts on polymers.
Globally the physical explanation is not unique, and is related to the material nature (metal, polymer, wood…). For metals this can be explained by the kinetic of development of dislocations, twining, and/or phase transformation witch may depend on the strain rate.
In summary, there is no a unique explanation of the increase of stress as strain rate increase.
In my opinion stresses are a manifestation of a momentum flux. This flux is created by a disturbance in the flow field and try to balance things (take them to equilibrium). The higher the disturbance (unbalance) the higher the flux must "work" to balance things again. The relation between the flux (stresses) and the gradients (strain rate) are not necessarily linear because the microstructure of the material may change during this transport process and hence the material property that links the flux with the gradient.
This concept may be applied to continuum mechanics (both solids and fluids). All constitutive models (Newton's viscosity law, Fourier's law of heat conduction, Fick's law for diffusion of mass and so on) are a manifestation of this tendency. The tendency to balance things through a certain flux created by an unbalance (gradient) in the system.
Very interesting question from a philosofical perspective.
Best regards, my friend!!
I am not sure about your question .... Are you talking about the Newtonian model that introduces a linear relation between the stress tensor and the velocity gradient? Not that the proportionality factor is a function of temperature, for high speed velocity the variation can be relevant.
Dear Purnashish,
Your question is not valid for all materials. Some materials do not show strain rate dependent hardening. To find an answer to your question, please read the attached article for materials with alpha-Fe.
Dear Muhammad Niazi sir,
I am taking about the aluminum alloy and mild steel.I don't want to know the exception. I want to know why is happening? why flow stress of some material increases with increase of strain rate?
The hardening is a competition between dislocation storage and annihilation. The rate at which these phenomena occur is influenced by the micro-structure / crystal type / precipitates etc. That is why you have to look at specific material type. For instance some aluminum alloys can also have negative strain rate sensitivity, see attachment.
A good question!
For metals which harden by the development of dislocations, the increase of the rate of deformation induces a multiplication of the dislocations (increase of their density). This causes the increase of work hardening and consequently the increase of the stress. This is the physical application.
In addition, at high deformation rates, a part of the deformation energy is converted into heat, which softens the material, which creates a competition between work-hardening and thermal softening.
For polymers (amorphous or semi-crystalline), another physical explanation must be given, in relation to their microstructure. For example, for PMMA the strain rate increases the flow stress, but I think it is not due to dislocation development!? See experts on polymers.
Globally the physical explanation is not unique, and is related to the material nature (metal, polymer, wood…). For metals this can be explained by the kinetic of development of dislocations, twining, and/or phase transformation witch may depend on the strain rate.
In summary, there is no a unique explanation of the increase of stress as strain rate increase.
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