Method and apparatus for determining preexisting stresses based on indentation or other mechanical probing of a material

A method of determining the preexisting stress in a stressed section of a material, comprising:

• obtaining indentation data from first and second indentations of substantially the same indentation load, the first indentation being of the stressed section of the material and the second indentation being of a second section having a known stress of one of the material and a substantially similar material, the indentation data including at least a first depth of indentation of the first indentation and a second depth of indentation of the second indentation;
• obtaining additional data including one of:
• a) the indentation load and the area of the second indentation;
• and b) other data that can allow the determination of the hardness that is characteristic of the material;
• and
• determining the stress from the data.

A method of determining the preexisting stress in a stressed section of a test material using first and second indentations, the test material being one of an elastoplastic material and/or a material exhibiting strain hardening, comprising:

• obtaining indentation data from first and second indentations with at least one sharp indenter, the first indentation being of the stressed section of the test material and the second indentation being of a second section having a known stress of one of the test material and a substantially similar material, the indentation data including at least the area of indentation of the first indentation and the area of indentation of the second indentation;
• obtaining additional data including one the following:
• an indentation load of one of the indentations;
• and other data that can allow the determination of the hardness that is characteristic of the material;
• and
• determining the stress from the data.

A method of determining the stress in a stressed section of a material, comprising:

• (a) obtaining first data from the indentation of the stressed section with an indenter, the first data including at least a load P.sub.s and a depth of penetration h.sub.s ;
• (b) obtaining second data characteristic of the material, the second data including Young's modulus (E), the yield strength (.sigma.y), and one of the stress at approximately 29% plastic strain (.sigma.u) and the strain hardening exponent (.eta.);
• (c) determining the hardness P.sub.ave ;
• (d) determining (h.sub.o).sup.2 =P.sub.s {.sigma.y(1+.sigma.u/.sigma.y)C*(1+ln((tan .alpha.)E/3.sigma..sub.y))}.sup.-1
• where C* and tan .alpha. depend on the type of the indenter;
• (e) determining the ratio R equivalent to R=(h.sub.s).sup.2 /(h.sub.o).sup.2 ;
• (f) determining the stress in satisfaction of the following formulae;
• if R<1;
• R={1+(geomf)stress/P.sub.ave }.sup.-1
• if R>1;
• R={1-stress/P.sub.ave }.sup.-1
• where geomf=sin .alpha.,
• and .alpha. is related to the angle of indentation of the indenter.

A method of determining the stress in a stressed section of a material, comprising:

• (a) obtaining first data from the indentation of the stressed section with an indenter, the first data including at least a penetration h.sub.s ;
• (b) obtaining second data characteristic of the material, the second data including Young's modulus (E), the yield strength (.sigma.y), and one of the stress at approximately 29% plastic strain (.sigma.u) and the strain hardening exponent(h);
• (c) determining the hardness P.sub.ave, where determining the hardness includes one of
• 1) obtaining first data including the load P.sub.s and the corresponding indentation area A.sub.s and determining the hardness P.sub.ave =P.sub.s /A.sub.s ;
• and
• 2) otherwise obtaining the known hardness value for the material;
• (d) determining (P.sub.o) from P.sub.o =(h.sub.s).sup.2 .sigma.y(1+.sigma.u/.sigma.y)C*{1+ln((tan .alpha.)E/3.sigma.y) }
• where C* and tan .alpha. depend on the type of the indenter
• e) determining the ratio R, where determining R includes one of
• 1) determining A.sub.o from A.sub.o =P.sub.o /P.sub.ave and determining R=A.sub.s /A.sub.0, where the first data includes the area of indentation A.sub.s and;
• 2) determining R=P.sub.s /P.sub.0, where the first data includes the load of indentation P.sub.s
• (f) determining the stress in satisfaction one of the following formulae
• if R<1;
• R={1+stress/P.sub.ave }.sup.-1
• if R>1;
• R={1-(geomf)stress/P.sub.ave }.sup.-1
• where geomf=sin(.alpha.), and .alpha. is related to the angle of indentation of the indenter.

A method of determining the stress in a stressed section of a material, comprising:

• (a) obtaining a loading curve of load P verses penetration h from the indentation with a known indenter of the stressed section:
• (b) fitting the loading curve to a polynomial expression of the form B.sub.1 h.sup.2 +B.sub.2 h.sup.3 to determine first and second constants B.sub.1 and B.sub.2 ;
• (c) based on the known properties of the indenter determining at least one additional constant B.sub.3 from B.sub.1 ;
• (d) obtaining a value for the yield strength (.sigma.y) characteristic of the material;
• (e) determining the stress G in the section of material as a function of the at least one additional constant B.sub.3 and .sigma.y.

A method of determining stress at the surface of a stressed section of a material and of determining the variation of stress with penetration, comprising:

• (a) obtaining a loading curve of load P versus position h from the indentation with an indenter of the section of material;
• (b) fitting the loading to curve to the polynomial expression B.sub.1 h.sup.2 +B.sub.2 h.sup.3 ;
• to obtain the constants B.sub.1 and B.sub.2 ;
• (c) determining third and fourth constants B.sub.3 and B.sub.4 in satisfaction of the formulas
• B.sub.3 =B.sub.1 /[11.88(tan .gamma.).sup.2 ]
• B.sub.4 =B.sub.2 /[8.sqroot.3(tan .gamma.).sup.3 ]
• where g is a known angle of the indenter,
• (d) obtaining a value for the yield strength (sy) of the material;
• (e) determining at least one of the magnitude of the stress at the surface of the section of material, G, and the magnitude of the rate of change of the stress with penetration, G, in satisfaction of the formulas
• B.sub.3 =-G.GAMMA.and (B.sub.4)=(.sigma.y).sup.2 -G.sup.2.
• 50.

A method of determining the residual plastic strain in a plastically-strained section of a material, comprising:

• (a) obtaining first data from the indentation of the section with an indenter, the first data including a penetration of (h) and a load (P) on the indenter;
• (b) obtaining second data characteristic of the material;
• (c) determining the residual yield strength as a function of the second data and the first data;
• and
• (d) determining the plastic strain from the residual yield strength.

An apparatus for determining the preexisting stress in a stressed section of material, comprising:

• a data processor, said data processor including program means for determining the stress in a stressed section of a material from first data and from second data characteristic of the material, said first data obtained from an indentation test on the stressed section and including at least a loading (P) versus penetration (h) curve and said second data including the yield strength of the material, said data processor further including means for fitting the loading to curve to a polynomial expression of the form B.sub.1 h.sup.2 +B.sub.2 h.sup.3 to determine at least first and second constants B.sub.1 and B.sub.2
• means for determining at least one additional constant B.sub.3 from B.sub.1 ;
• and
• means for determining the stress G in the section of material as a function of the at least one additional constant B.sub.3 and the yield strength .sigma.y.

Apparatus for determining the plastic strain in a section of material that has plastically yielded, comprising:

• a data processor, said data processor including
• means for determining from first data obtained by indenting the section with an indenter and from second data characteristic of the material the stress in the stressed section, the first data including a penetration (h) and a load (P) on the indenter, said means including
• means for determining the residual yield strength as a function of the second data and the first data;
• and
• means for determining the plastic strain in the section of the material from the residual yield strength and said second data.

A method of determining the preexisting stress in a stressed section of a material from data obtainable via one indentation of the stressed section, comprising:

• obtaining first data from indentation of the stressed section, the first data including at least two of the following:
• the area of indentation, the depth of indentation, and the indentation load;
• and
• determining the preexisting stress as a function of the first data and other data that is determinable other than via indentation with the indentor, and wherein the measurement of the deformation of the material via strain, tensiometric gauges or an extensometer placed in the vicinity of the area of contact between the indentor and the stressed section is not required to determine the stress.

A method of determining the preexisting stress in a stressed section of material including using first and second indentations, comprising:

• obtaining indentation data from the first and second indentations to a substantially similar depth of penetration, the first indentation being of the stressed section of material and the second indentation being of a second section having a known stress of one of the material and a substantially similar material, the indentation data including at least one of a first indentation load and a first indentation area of the first indentation and including at least one of a second indentation area and a second indentation load of the second indentation;
• obtaining additional data that can allow determination of the hardness of the material;
• and
• determining the stress from the data.