As per Wikipedia," Flow stress is defined as the instantaneous value of stress required to continue plastically deforming the material - to keep the metal flowing. It is the middle value between yield strength and ultimate strength of the metal as a function of strain".However I do not understand what it means by "keep the metal flowing".Please answer this with reference to the context.
The term 'flow' stress recognizes the inherent irreversible nature of plasticity. For instance, the flow of fluids is associated with an apparent lack of memory of their previous state. In other words, once water flows on a surface, it completely loses its shape and cannot be brought back to its original state. You can refill it in a cup but the structural state of water has completely changed. Fluids are therefore inherently non- elastic. You cannot define a elastic modulus as it resists complete recovery to their original states. However, fluids can have a flow stress depending on their viscosity. For example you can notice that its easy to make water flow but you need to apply some force to make grease flow (there is usually a time dependence associated with the force applied on liquids to make them flow, but we will not go into the details of viscoplasticity in this question).
Much like liquids, metals undergo irreversible shape change or plastic flow above the yield stress. Below the yield stress, it would be incorrect to define any value of stress as flow stress. Next, we examine the difference between yield stress and flow stress. Both terms cannot be used interchangeably, except in some cases. The yield stress is used to define the onset of plastic flow. Beyond this the metal can do the following things depending on what deformation mechanisms are active.
1. If the metal has coherent/incoherent second phase precipitates or provides some other microstructural barriers for dislocation motion (solid solution strengthening, dislocation-dislocation interactions or dislocations-grain boundary interactions), they become stronger with increasing strain. This is called strain hardening and the stress obeys an exponential relationship with strain : Stress_f = Constant * (strain_f) ^n. Here 'n' is defined as the strain hardening exponent. In such a case, the stress required to continue deforming the material beyond the yield strain requires a stress that is higher than the yield stress. One can also note that the flow stress increases with strain but the yield stress or yield strength is a material property. (stress_f is defined as the flow stress here)
Although, barring the exponential term, this relationship appears to have some similarity with the Hooke's law for elasticity, they are not at all comparable. Note that plastic flow is inherently irreversible. Let us say you are compressing a solid plastically, you cannot simply reverse the loading direction and expect the material to deform plastically at a lower stress (although sometimes it does happen due to the Bauschinger effect). This is why when you unload the specimen, the unloading happens according to Hooke's law of elasticity and only the elastic part of the deformation is recovered.
2. If the material is elastic-perfectly plastic, i.e. if it does not strain harden, then the material can be strained at the same value of stress. In such a case the flow stress and yield stress are approximately equal and the flow stress is also constant.
3. If a strain softening material is deformed then the flow stress decreases with increasing strain and flow stress is always lower than the yield stress.
If this explanation is not fully clear, flow stress can be explained in another way. Consider a case where a specimen is loaded to some stress, sigma_n, above the yield stress, sigma_y, and the material strain hardens. Thereafter, the specimen is unloaded. On fully unloading the specimen, the elastic part of the strain completely recovers. In case you reload the specimen, the onset of plasticity will require a stress sigma_n, which is higher than the material yield stress sigma_y. It now becomes easy to reconcile with the definition of flow stress.
The term 'flow' stress recognizes the inherent irreversible nature of plasticity. For instance, the flow of fluids is associated with an apparent lack of memory of their previous state. In other words, once water flows on a surface, it completely loses its shape and cannot be brought back to its original state. You can refill it in a cup but the structural state of water has completely changed. Fluids are therefore inherently non- elastic. You cannot define a elastic modulus as it resists complete recovery to their original states. However, fluids can have a flow stress depending on their viscosity. For example you can notice that its easy to make water flow but you need to apply some force to make grease flow (there is usually a time dependence associated with the force applied on liquids to make them flow, but we will not go into the details of viscoplasticity in this question).
Much like liquids, metals undergo irreversible shape change or plastic flow above the yield stress. Below the yield stress, it would be incorrect to define any value of stress as flow stress. Next, we examine the difference between yield stress and flow stress. Both terms cannot be used interchangeably, except in some cases. The yield stress is used to define the onset of plastic flow. Beyond this the metal can do the following things depending on what deformation mechanisms are active.
1. If the metal has coherent/incoherent second phase precipitates or provides some other microstructural barriers for dislocation motion (solid solution strengthening, dislocation-dislocation interactions or dislocations-grain boundary interactions), they become stronger with increasing strain. This is called strain hardening and the stress obeys an exponential relationship with strain : Stress_f = Constant * (strain_f) ^n. Here 'n' is defined as the strain hardening exponent. In such a case, the stress required to continue deforming the material beyond the yield strain requires a stress that is higher than the yield stress. One can also note that the flow stress increases with strain but the yield stress or yield strength is a material property. (stress_f is defined as the flow stress here)
Although, barring the exponential term, this relationship appears to have some similarity with the Hooke's law for elasticity, they are not at all comparable. Note that plastic flow is inherently irreversible. Let us say you are compressing a solid plastically, you cannot simply reverse the loading direction and expect the material to deform plastically at a lower stress (although sometimes it does happen due to the Bauschinger effect). This is why when you unload the specimen, the unloading happens according to Hooke's law of elasticity and only the elastic part of the deformation is recovered.
2. If the material is elastic-perfectly plastic, i.e. if it does not strain harden, then the material can be strained at the same value of stress. In such a case the flow stress and yield stress are approximately equal and the flow stress is also constant.
3. If a strain softening material is deformed then the flow stress decreases with increasing strain and flow stress is always lower than the yield stress.
If this explanation is not fully clear, flow stress can be explained in another way. Consider a case where a specimen is loaded to some stress, sigma_n, above the yield stress, sigma_y, and the material strain hardens. Thereafter, the specimen is unloaded. On fully unloading the specimen, the elastic part of the strain completely recovers. In case you reload the specimen, the onset of plasticity will require a stress sigma_n, which is higher than the material yield stress sigma_y. It now becomes easy to reconcile with the definition of flow stress.
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