Consider dynamic (rapid) indentation of a rigid-perfectly plastic material by a sharp rigid cone of apex angle 90 degrees. The hardness value obtained from such a test is called the dynamic hardness of the material. The dynamic indentation can be modeled as a process in which the full indentation load is applied instantaneously. Assume the static hardness of this rigid-perfectly plastic material measured in a typical hardness test (where the load is slowly increased from zero) with the same cone to be H. Estimate the dynamic hardness of the material in terms of the static hardness H. Note: Both static hardness and dynamic hardness are defined as the load divided by the projected area of the indentation. (Hint: Consider work balance in the dynamic hardness test – external work done by the applied force is equal to the internal deformation work. The latter can be thought as pdV work, with p being identified with the resisting pressure (= static hardness H) of the material, and V with the volume of material displaced by the indenter).
Consider dynamic (rapid) indentation of a rigid-perfectly plastic material by a sharp rigid cone of apex angle 90 degrees. The hardness value obtained from such a test is called the dynamic hardness of the material. The dynamic indentation can be modeled as a process in which the full indentation load is applied instantaneously. Assume the static hardness of this rigid-perfectly plastic material measured in a typical hardness test (where the load is slowly increased from zero) with the same cone to be H.
Estimate the dynamic hardness of the material in terms of the static hardness H.
Note: Both static hardness and dynamic hardness are defined as the load divided by the projected area of the indentation.
(Hint: Consider work balance in the dynamic hardness test – external work done by the applied force is equal to the internal deformation work. The latter can be thought as pdV work, with p being identified with the resisting pressure (= static hardness H) of the material, and V with the volume of material displaced by the indenter).
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