Method of determining elastic and plastic mechanical properties of ceramic materials using spherical indenters
AssigneeThe United States of America as represented by the Secretary of the Interior
InventorThomas A. Adler
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Abstract
The invention pertains a method of determining elastic and plastic mechanical properties of ceramics, intermetallics, metals, plastics and other hard, brittle materials which fracture prior to plastically deforming when loads are applied. Elastic and plastic mechanical properties of ceramic materials are determined using spherical indenters. The method is most useful for measuring and calculating the plastic and elastic deformation of hard, brittle materials with low values of elastic modulus to hardness.
Claims20
A process for measuring the plastic and elastic deformation of a hard, brittle material having a strain to failure in a tensile test of about 0.1 or less which comprises:
- (a) indenting a hard, brittle material with a rigid, solid, spherical indenter having a sphere radius of at least about 2 micrometers and a hardness of at least about 1/2.5 times the hardness of the brittle material;
- and
- (b) measuring at least one of the contact diameter plastic deformation and contact depth plastic deformation resulting from the indenting;
- and
- (c) calculating K.sub.2 and m.sub.2 for the spherical indenter;
- and
- (d) calculating K.sub.1 and m.sub.1 for the brittle material according to at least one of the equations:
- ##EQU40## wherein ##EQU41## B.sub.p =1.18028-0.85730 m.sub.1 +0.17761 m.sub.1.sup.2 C.sub.1 =2.87339+0.19495 m.sub.1 +0.63433 m.sub.1.sup.2
- C.sub.2 =7.02098+0.24729 m.sub.1 +0.13521 m.sub.1.sup.2
- a is the contact radius of the brittle material, C.sub.1, and C.sub.2 are deflection constants, B.sub.p is the profile shape ratio;
- k.sub.1 is the elastic constant for the brittle material, k.sub.2 is the elastic constant for the spherical indenter, u is the mean pressure applied;
- K.sub.1 is the Meyer's law constant for the brittle material, K.sub.2 is the Meyer's law constant for the spherical indenter, m.sub.1 is the strain hardening exponent for the brittle material, m.sub.2 is the strain hardening exponent for the spherical indenter, D is the diameter of the spherical indenter;
- d is the contact depth;
- L is the applied load, E.sub.1 is the elastic modulus for the brittle material, E.sub.2 is the elastic modulus for the spherical indenter, and v.sub.1 is the Poisson's ratio for the brittle material and v.sub.2 is the Poisson's ratio for the spherical indenter.
A method of fracturing a brittle material and determining the elastic and plastic deformation thereof which comprises
- (A) providing a hard, brittle material having a strain to failure in a tensile test of about 0.1 or less;
- (B) providing a rigid, solid, spherical indenter having a sphere radius of at least about 2 micrometers and a hardness of at least about 1/2.5 times the hardness of the brittle material;
- and
- (C) deforming the hard, brittle material by indenting it with the spherical indenter;
- (D) measuring at least one of the contact diameter plastic deformation and contact depth plastic deformation resulting from the indenting;
- and
- (E) calculating K.sub.2 and m.sub.2 for the spherical indenter;
- and
- (F) calculating K.sub.1 and m.sub.1 for the brittle material according to at least one of the equations:
- ##EQU42## wherein ##EQU43## B.sub.p =1.18028-0.85730 m.sub.1 +0.17761 m.sub.1.sup.2 C.sub.1 =2.87339+0.19495 m.sub.1 +0.63433 m.sub.1.sup.2
- C.sub.2 =7.02098+0.24729 m.sub.1 +0.13521 m.sub.1.sup.2
- a is the contact radius of the brittle material, C.sub.1, and C.sub.2 are deflection constants, B.sub.p is the profile shape ratio;
- k.sub.1 is the elastic constant for the brittle material, k.sub.2 is the elastic constant for the spherical indenter, u is the mean pressure applied;
- K.sub.1 is the Meyer's law constant for the brittle material, K.sub.2 is the Meyer's law constant for the spherical indenter, m.sub.1 is the strain hardening exponent for the brittle material, m.sub.2 is the strain hardening exponent for the spherical indenter, D is the diameter of the spherical indenter;
- d is the contact depth;
- L is the applied load, E.sub.1 is the elastic modulus for the brittle material, E.sub.2 is the elastic modulus for the spherical indenter, and v.sub.1 is the Poisson's ratio for the brittle material and v.sub.2 is the Poisson's ratio for the spherical indenter.
Dependencies are inferred from the claim text.