ES2239507A1 - Method for evaluation of mechanical properties of material from topographic characteristics of pointed indentation, involves evaluating tension of flow and coefficient of hardening by uniaxial deformation of material - Google Patents

Abstract

The method involves inducing deformation in a material that is to be evaluated by application of a mechanical load with a relatively rigid penetrator. Tension of flow and coefficient of hardening are evaluated by uniaxial deformation of the material from measurement of topographic characteristics.

Description

Methodology for property evaluation mechanics of materials from the characteristics topographical of a pointed indentation.

Technical sector

This invention allows to infer properties fundamental mechanics of materials by testing indentation, in which the value is exclusively taken into account of hardness and the deformation existing around the footprint of indentation The proposed procedure is useful in cases where topographic characterizations are made around the footprint. Its particularity with respect to other procedures lies in its total independence of the load curve knowledge (P) - penetration depth (h_ {s}) of indenter in the material sample. This curve can be obtained through advanced instrumented indentation techniques. In a optional embodiment, the procedure explicitly uses the P-h_ {s} curve instead of features topographical in the evaluation of mechanical properties.

State of the art

The invention relates to the determination of mechanical properties of materials by indentation tests  Pointy Indentation tests are widely used in the characterization of materials and components. They consist of application of a mechanical load with a solid geometry known (referred to as indenter or penetrator), on a sample flat material whose mechanical characteristics are wanted evaluate. To the extent that the load is applied, the indenter produces plastic deformation that results in a footprint or imprint permanent on the surface. Once the test is done, it is measured the area of the imprint and the hardness of the material is calculated as the quotient between the maximum applied load and the measured area.

In recent years, instrumented techniques have been developed with which the applied load (P) and the penetration depth (h s) of the indenter in the sample are measured in situ during the indentation test. These techniques are relevant in the microelectronic industry and, in particular, in the characterization of coatings. These tests are carried out in a load range typically less than 1 N, so the technique conventionally refers to the term nano-indentation ( US Pat. No. 4,848,141, Oliver et al .; US Pat. No. 5, 359, 879, Oliver et al .; US Pat No. 4, 820, 051, Yanagisawa et al .; US Pat No. 4,627,096, Gattoni et al .; US Pat No. 4, 699, 000, Lashmore et al .; US Pat No. 4, 852, 397, Haggag; US Pat. No. 6,134,954, Suresh et al .; Alcalá et al., J. Mater. Res. P. 1390 (1998); Oliver et al. J. Mater. Res p. 1564 (1992) ).

As evidenced in the following documents, indentation techniques allow to measure hardness as well as evaluate fundamental mechanical properties for the design: M. Mata et al., J. Mater. Res. Vol. 17, 964 (2002); D. Tabor, Hardness of Metals, Clarendon Press, United Kingdom, 1951; H. O'Neill, Hardness Measurements of Metals and Alloys, Chapman Hall, 1951; MF Doener and WD Nix, J. Mater. Res. Vol. 1, p. 601 (1986); WC Oliver and GM Pharr, J. Mater. Res. Vol. 7, p. 1564, (1992); YT Cheng and CM. Cheng, J. Appl. Phys. Vol 84, p. 1284 (1998); YT Cheng and CM. Cheng, Appl. Phys. Lett. Vol. 73, p. 614 (1998); YT Cheng and CM. Cheng, Int. J. Solids Struct. Vol. 36, p. 1231 (1999); YT Cheng and CM. Cheng, J. Mater. Res. Vol. 14, p. 3493, (1999); J. Alcalá et al., J. Mater. Res., Vol. 13, p. 1390 (1998); S. Suresh et al., US Patent No. 6,134,954 (2000); J. Alcalá, J. Am. Ceram. Soc. Vol. 83, p. 1977 (2000); K. Tunvisut et al., Int. J. Solids Struct, Vol 38, p. 335 (2001; J. Alcalá et al., Mater. Sci. Engng A. vol 316, p. 1 (2001); M. Mata et al., Phil. Mag. A Vol 82, p. 1831 (2002); K. Matsuda, Phil. Mag. A, vol. 82, p. 1941 (2002); NX Randall, Phil. Mag. A Vol. 82, p. 1883 (2002); SV Hainsworth et al., J. Mater. Res., Vol 11 No. 8, p. 1987 (1996); WC Oliver, J. Mater. Res., Vol 7 No. 6, p. 1564 (1992); WH Robinson et al., J. Mater. Sci ., vol 12, No. 10, p. 1961 (1977); M. Dao et al., Acta Mater, vol 49, p. 3899 (2001); J. Alcalá et al., Acta Mater. Vol 48, p .3451 (2000); US Pat. No. 5, 490, 416, Adler) .

Conventionally, indentation tests are classified according to the load range used or according to the geometry of the indenter that is used to induce the footprint. By way of indication, those tests are referred to as nano-indentation carried out in a load range of less than 0.5 Newton; micro-indentation to those tests performed between 0.5 and 100 Newton; and macro-indentation to tests in which the applied loads exceed 500 Newton. In in relation to the geometry of the penetrator, the tests are classified as of pointed or spherical indentation. In the first ones they use conical or pyramidal penetrators and, in the seconds, spherical indenters. The most used pyramid penetrators They are called Vickers and Berkovich depending on their characteristics  geometric

In the context of the works cited previously, the object of the patent is the use of indentation techniques to evaluate mechanical properties fundamentals of materials that, conventionally, could only Obtained by uniaxial mechanical tests. This aspect is relevant in engineering since structural design requires know a priori the mechanical behavior of the materials that They make up a certain component. Uniaxial tests Conventional require the use of samples (specimens) of considerable dimensions that are hardly obtainable in a Significant number of practical applications. Since the limitation  of the sample size is much less severe in trials of indentation, its development is relevant in regard to the mechanical characterization of materials and structures. He The process object of the patent is therefore useful in the structural integrity assessment and quality control of coatings, welded joints and, in general, components used in the petrochemical industry, as in sheet metal thin wall for the transport and aerospace industries.

The properties object of this procedure are the creep stress, also known as creep limit or elastic limit, (\ sigma_ {ys}) and the coefficient of hardening by uniaxial deformation (n). The proposed methodology is applicable both in conventional tests of hardness and in advanced tests of instrumented indentation, in which the P-h s curve is measured in situ .

Brief Description of the Invention

This invention consists of a precise method for the evaluation of the values of the \ sigma_ {ys} yn of materials from (i) conventional hardness measurements, and (ii) of the deformation that is generated around the indentation fingerprint ( see Fig. 9). The invention relates exclusively to pointy indentation tests, carried out with conical or pyramidal indenters Vickers and Berkovich. A novel aspect of the method is that, so far, existing methodologies to infer \ sigma_ {ys} and starting from indentation techniques required the measurement of the P-h_ {s} curve of the material (US Pat. No. 6,134,954, Suresh et al .; Alcalá et al., J. Mater. Res. (1998); YT. Cheng and CM. Cheng, J. Appl. Phys. (1998); M. Dao et al., Acta Mater. (2001)) . In the preferred embodiment of the invention, knowledge of the P-h s curve is replaced by an evaluation of the deformation around the imprint, which can be obtained independently of the P-h s curves using, for example, microscopy of atomic forces. Although there are methodologies for evaluating mechanical properties that use concepts similar to those proposed in this invention, these procedures differ from the present invention in that they are only applicable for: (i) spherical indentation tests (US Pat. No. 5,490,416, Adler; Alcalá et al., J. Mater. Res. (1998)) and (ii) relatively soft materials whose response to contact is called "completely plastic" as reported by M. Mata et al., J. Mater. Res. (2002) and J. Alcalá et al., Acta Mater. (2000)) .

Detailed description

The hardness (H) of the material is calculated as the quotient between the maximum load applied by the indenter (P_ {max}) and the area (A_ {max}) of the remaining imprint or imprint in the indented material:

(1) H = \ frac {P_ {max}} {A_ {max}}

The surface deformation around the Indenter can be of two types. First, it is considered that the indented material may suffer stacking in the periphery of the contact, so the actual area of the footprint is larger than that estimated from the shape (geometry) of the indenter. Second, subsidence of the material can develop in the periphery of the contact, so the real area of the footprint is less than that calculated from the shape (geometry) of the indenter The magnitude of the surface deformation is calculated at from the \ sqrt {\ alpha} parameter, which is a quotient between penetration depths For this it is necessary to define the vertical distance between the tip of the indenter and the height in where the contact area (h) is located, as well as the distance vertical between the tip of the indenter and the original surface of the indented material (h_ {s}). You have then that

(2) \ sqrt {\ alpha} = \ frac {h} {h_ {s}}

In the preferred embodiment of the procedure, indentation tests are carried out in a range of loads in the that the hardness (H) remains constant. That is, in a range of loads of sufficient magnitude so that in the quotient between P_ {max} and A_ {max} be independent of the load P_ {max} used to induce the area footprint A_ {max}. Likewise, it consider that the P-h_ {s} curve during the stage of cargo follows a parabolic relationship (Kick's law), with which have to:

(3) P = Kh_ {s} 2

A characteristic of the tension curve (\ sigma) - uniaxial deformation (ε) to be inferred through the indentation tests is the tension value uniaxial to a total deformation of 10%. This mechanical tension, \ sigma_ {r}, is called representative tension and is calculated at from Young's (E) module of indented material and hardness (H) solving the following equation:

(4) \ frac {H} {\ sigma_ {r}} = - \ text {0.0023} \ left (1n \ left (\ frac {E} {\ sigma_ {r}} \ right) \ right) ^ {4} + \ text {0.0647} \ left (1n \ left (\ frac {E} {\ sigma_ {r}} \ right) \ right) ^ {3} - \ text {0.6817} \ left (1n \ left ( \ frac {E} {\ sigma_ {r}} \ right) \ right) ^ {2} + \ text {3.1968} \ left (1n \ left (\ frac {E} {\ sigma_ {r}} \ right) \ right) - \ text {2.9261}

From the value of the representative voltage (\ sigma_ {r}), the coefficient of hardening by uniaxial deformation (n) resolving the equation:

(5) \ sqrt {\ alpha} = A + B \ exp \ left \ {- \ frac {\ sigma _ {r} / E} {D} \ right \}

where

A = 8.7760 n3 - 6.7180 n2 + 1.0478 n + 0.8148

B = -7.7892 n 3 + 6.8690 n 2 - 2.0273 n + 0.4790

D = -0.35359 n 3 + 0.40038 n 2 - 0.05926 n + 0.01426

Finally, using \ sigma_ {r}, n and E, you calculate the creep stress \ sigma_ {ys} of the material through the expression:

(6) \ sigma_ {ys} = \ left (\ frac {\ sigma_ {r}} {E ^ {n} (0.1) ^ {n}} \ right) ^ {\ tfrac {1} {1-n}}

In the preferred application of the procedure, assume that the \ sigma - \ varepsilon curve can approximate according:

10

Description of the drawings

This report is accompanied by schemes and results. that facilitate the understanding of the nomenclature used and the inferred uniaxial mechanical properties.

In the drawings, Fig. 1 represents the curve of stress (sig) - uniaxial deformation (ε) in which the properties \ sigma_ {ys}, n and Young's module are indicated E. Fig. 2 shows the geometries of the conical indenters, Vickers and Berkovich employed in the preferred embodiment of the invention. Fig. 3 schematizes a footprint under the action of the applied load, where the variables h and h_ {s} are defined in materials in which stacking ((1)) and sinking ((2)) occurs. Figs. 4 and 5 show topographies and typical contours of fingerprints (1) in Fig. 4 indicates stacking and (2) in Fig. 5 represents sinking). In Figs. 4 and 5 the contours or zero level curves (7) (from which the stacking or sinking). Figs. 6 and 7 show the projection of stacking (Fig. 6) and sinking (Fig. 7) on the sides of the edge (defined according to coordinate x in Fig. 4). The x axis is defined so that it coincides with the zero level curve (Fig. 4). Figure 8 shows a P-h_ {s} curve obtained for a hardness material H = 0.6 GPa by means of a test of pointed indentation. In Fig. 8 the arrows are indicated with loading and unloading stages of the test as well as the point of maximum load (P_ {max}). Fig. 9 shows the algorithm for application of the method developed in the invention ((4), (5), (6)). Finally, Fig. 10 presents a Vickers imprint on a 6061-T6 aluminum alloy. The defined area by imprint ((3)) it is referred to as A max in the patent.

Way of carrying out the invention

The preferred way of carrying out the invention it consists of contacting a pointed indenter (which interchangeably it can be conical, Vickers, or Berkovich) with a flat surface of material. The indenter is preferably of diamond or other material at least 2 times stiffer than the flat surface to indent. The indenter applies a load incremental on the surface that induces deformation irreversible (plastic) of the indented material ((3) Fig. 10). A once the maximum load has been applied, either in the range of nano-indentation, microindentation or macro-indentation, the indenter withdraws downloading gradually.

A topographic characterization of the remaining imprint or imprint is then obtained (Figs. 4 and 5). Without neglecting other techniques, this characterization can be performed using an atomic force microscope ( NX Randall, Phil. Mag. A Vol. 82, p. 1883 (2002) ) or from successive sweeps obtained with a contact profilometer ( J. Alcalá et al., Acta Mater. Vol 48, p.3451 (2000) ). This characterization demonstrates that the materials can suffer stacking ((1) Fig. 4 and Fig. 6) or sinking ((2) Fig. 5 and 7). The Amax value of the imprint ((3) Fig. 10) is then measured and the hardness H is calculated according to equation (1).

The value of \ sqrt {\ alpha} is estimated under the maximum load applied by the indenter. For indenters Vickers and Berkovich, surface deformation is projected (remaining after discharge) on the sides of the imprint as illustrated in Figs. 6 and 7. The average value of the vertical displacement of the material around the sides of the imprint, h_ {med}, by some procedure numerical integration of stacking ((1)) or sinking ((2)) on the 5 sides of the imprint (see Figs. 6 and 7). In trials of conical indentation, surface deformation is constant around the footprint so it is not necessary to apply the integration procedure

From the value of h_ {med} you get to then the amount of stacking or sinking that exists under the maximum load applied by the indenter. To do this, it first calculate the magnitude \ Deltah_ {med} that quantifies the vertical recovery of the indented surface. This phenomenon of Recovery occurs during the discharge of the indenter. The variable \ Deltah_ {med} is calculated as:

(8) \ Deltah_ {med} = \ frac {P_ {max} (1- \ nu2 {}}} {c \ sqrt {A_ {max}} E}

where E and \ nu are, respectively, Young's modulus and Poisson coefficient of indented material; P_ {max} the maximum load applied by the indenter during the test; A_ {max} the footprint area remnant, (3) Fig. 10; and c is a constant whose value is 1,142 for the indenter Vickers, 1,167 for the Berkovich and 1,128 for a cone on whose tip an angle of 70.3 °.

With the values of h_ {med}, \ Deltah_ {med} and the maximum depth of the footprint (h_ {m}) measured from the contour or zero height level, \ sqrt {\ alpha} is calculated through:

(9) \ sqrt { \ alpha} = \ frac {(h_ {m} + h_ {med})} {(h_ {m} + \ Delta h_ {med})}

Once the values of \ sqrt {\ alpha} are known and H, equations (4), (5) and (6) are solved in order to obtain the properties \ sigma_ {ys} and n of the indented material ((4), (5), (6) in Fig. 9).

The invention can also be realized from the P-h s curve obtained by a test of instrumented indentation, and the value of H measured experimentally by equation (1). To do this, it is done an adjustment to the Kick's law (Equation (3)) of the loading stage of the P-h_ {s} curve. This setting supplies the value of K. To find α the expression is used:

(10) \ alpha = \ frac {K} {f H}

where f is worth 24.50 for Vickers or conical indenters with 70.3 ° internal half angle, and 24.56 for Berkovich

Within the margin of the experimental error itself of the techniques used, the value of \ sqrt {\ alpha} obtained using curves P-h_ {s} and hardness H is coincident with that calculated from equation (9). Finally, as stated in the preferred embodiment of the invention (4, 5, 6 in Fig. 9), equations (4), (5) are solved and (6) with the values of \ sqrt {\ alpha} and H in order to extract the properties \ sigma_ {ys} and n of the indented material.

The embodiment of the invention. The example refers to an aluminum alloy 6061-T6 whose values of E, \ sigma_ {ys} and n obtained from the conventional uniaxial test are, respectively, 70 GPa, 300 MPa and 0.079. The realization of the invention by a Vickers indentation test up to a load 100 Newtons maximum provides a footprint with h_ {med} = 8.26 \ mum. Hardness H is 1.20 GPa (equation (1)). The estimated value of \ Deltah_ {med} from equation (8) is 3.94 \ mum, with what the properties \ sigma_ {ys} and n obtained by means of Equations (4), (5) and (6) are, respectively, 377 MPa and 0.059. These mechanical properties approximate those obtained directly from the conventional uniaxial test. The value of K found from the P-h_ {s} curve is 34 GPa (equation (3)), in good agreement with the relationship between H, \ sqrt {\ alpha} and K prescribed by equation (10). This agreement guarantees the alternative embodiment of the invention.

Claims (6)

1. A method to measure the voltage or limit of creep, \ sigma_ {ys}, and hardening coefficient by deformation, n, of a material from an indentation test made with a pointed penetrator. The method entails the performing at least the last of the following steps:

to)

to size the area of the imprint induced by the indenter in the material;

b)

calculation of H by equation:

H = \ frac {P_ {max}} {A_ {max}}

where A_ {max} is the area of the imprint and P_ {max} the maximum load applied by the penetrator;

C)

to size the amount of surface deformation around the imprint according to the parameter α;

d)

calculate the parameters \ sigma_ {ys} and n from the equations:

\ frac {H} { \ sigma_ {r}} = \ text {-0.0023} \ left (1n \ left (\ frac {E} {\ sigma_ {r}} \ right) \ right) ^ {4} + \ text {0.0647} \ left (1n \ left (\ frac {E} { \ sigma_ {r}} \ right) \ right) ^ {3} - \ text {0.6817} \ left (1n \ left ( \ frac {E} {\ sigma_ {r}} \ right) \ right) ^ {2} + \ text {3.1968} \ left (1n \ left (\ frac {E} {\ sigma_ {r}} \ right) \ right) - \ text {2.9261} Y \ sqrt {\ alpha} = A + B \ exp \ left \ {- \ frac {\ sigma_ {r} / E} {D} \ right \} where A = 8.7760 n3 - 6.7180 n2 + 1.0478 n + 0.8148 B = -7.7892 n 3 + 6.8690 n 2 - 2.0273 n + 0.4790 D = -0.35359 n 3 + 0.40038 n 2 - 0.05926 n + 0.01426 2. The method proposed in claim 1 in the one that the pointed penetrator is a Vickers pyramid. 3. The method proposed in claim 1 in the one that the pointed penetrator is a Berkovich type pyramid. 4. A method to measure the voltage or limit of creep, \ sigma_ {ys}, and hardening coefficient by deformation, n, of a material from an indentation test made with a pointed penetrator. The method entails the performing at least the last of the following steps:

to)

obtaining parameter K by load curve adjustment (P) - penetration depth (h_ {s}) to the following expression:

P = Kh_ {s} 2 ;

b)

calculation of H by equation:

H = \ frac {P_ {max}} {A_ {max}}

where A_ {max} is the area of the imprint and P_ {max} the load applied by the penetrator

C)

α calculation using the equation:

α = \ frac {K} {f H}

where f is worth 24.50 for Vickers or conical indenters with internal half angle of 70.3 °, and 24.56 for Berkovich;

d)

parameter calculation \ sigma_ {ys} and n from the equations:

\ frac {H} {\ sigma_ {r}} = - \ text {0.0023} \ left (1n \ left (\ frac {E} {\ sigma_ {r}} \ right) \ right) ^ {4} + \ text {0.0647} \ left (1n \ left (\ frac {E} {\ sigma_ {r}} \ right) \ right) ^ {3} - \ text {0.6817} \ left (1n \ left ( \ frac {E} {\ sigma_ {r}} \ right) \ right) ^ {2} + \ text {3.1968} \ left (1n \ left (\ frac {E} {\ sigma_ {r}} \ right) \ right) - \ text {2.9261} Y \ sqrt {\ alpha} = A + B \ exp \ left \ {- \ frac {\ sigma_ {r} / E} {D} \ right \} where A = 8.7760 n3 - 6.7180 n2 + 1.0478 n + 0.8148 B = - 7.7892 n3 + 6.8690 n2 - 2.0273 n + 0.4790 D = - 0.35359 n3 + 0.40038 n2 - 0.05926 n + 0.01426 5. The method proposed in claim 4 in the one that the pointed penetrator is a Vickers pyramid. 6. The method proposed in claim 4 in the one that the pointed penetrator is a Berkovich type pyramid.