ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation

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H18 1t 1t

1 t 2t

4 t

O 0 0 0

1t 1t

2 t

1 t 2t

3t 4t 5t 5t 6t 7t

1 t 2t

3t 4t 5t 5t 6t 7t

2014

T6 3t 4t 4t 5t 6t 8t

8 t 9t

O 0 0 0

1t 1t

2 t

3t 4t 5t 5t 6t 7t

7 t

T361

(a)

3t 4t 5t 6t 6t 8t

8 t 9t

2 t

3t 4t 5t 5t 6t 7t

7 t

T81

4 t 5t

7 t

8t 9t 10t

10 t

2024

T861

(a)

5t 6t 7t

8 t 9t

10t

11 t 11 t

2036

T4 … 1t 1t … … … … …

O 0 0 0 0

1t 1t

1 t

H12 0 0 0

1t 1t

1 t

H14 0 0 0 1t 1t

1 t

2 t

H16

1t 1t

1 t 2t

3 t

3003

H18 1t

1 t

2 t 3t 4t 5t 6t

O 0 0 0

1t 1t 1t

1 t

H32 0 0

1t 1t

1 t 1t

H34 0 1t 1t

1 t 1t 2t 2t

H36 1t 1t

1 t 2t

4 t

3004

H38 1t

1 t 2t

3t 4t 5t

5 t 6t

3105

H25 …

t t

… … … … …

O 0 0 0 0

1t 1t

1 t

H12 0 0 0

1t 1t

1 t

H14 0 0 0 1t

1 t

2 t

H16

1t 1t

1 t 2t

3 t

H18 1t

1 t

2 t 3t 4t 5t 6t

H32 0 0 0

1t 1t

1 t

H34 0 0 0 1t

1 t 1t 2t 2t

H36

1t 1t

1 t 2t

3 t

5005

H38 1t

1 t

2 t 3t 4t 5t 6t

O 0 0 0

1t 1t … …

H32 0 0 0 1t 1t

1 t

… …

5050

H34 0 0 1t

1 t 1t

2t … …

H36 1t 1t

1 t

2 t

3t … …

H38 1t

1 t 2t

3t 4t 5t … …

O 0 0 0

1t 1t

1 t 1t

H32 0 0 1t

1 t 1t 1t 1t

H34 0 1t

1 t

2t 2t

2 t 2t

H36 1t 1t

1 t 2t

3 t

4 t

5052

H38 1t

1 t 2t

3t 4t 5t

5 t 6t

O … …

1t 1t 1t

1 t 1t

5083

H321 … … 1t

1 t 1t 1t

2 t

O 0 0

1t 1t 1t

1 t 1t

H32 0

1 t 1t

2 t

H34

1 t

2 t

3 t

5086

H36 … … … 3t

3 t

4 t

O 0 0

1t 1t 1t

1 t 1t

H32 0

1 t 1t

2 t 3t

H34

1 t

2 t

3 t

H36 1t

1 t

2t 3t

3 t

4 t

5154

H38

1 t 2t

3t 4t 5t 5t

6 t 6t

H25 0 0 1t 2t … … … …

5252

H28 1t

1 t 2t

3t … … … …

O 0 0

1t 1t 1t

1 t 1t

H32 0

1 t 1t

2 t 3t

H34

1 t

2 t

3 t

H36 1t

1 t

2t 3t

3 t

4 t

5254

H38

1 t 2t

3t 4t 5t 5t

6 t 6t

O 0

1t 1t 1t

1 t 1t

H32

t t

1t 2t 2t

2 t

3t 4t

5454

H34

1 t

2 t

3 t

O … … … 1t

1 t 1t

2t 2t

5456

H321 … … … 2t 2t

2 t

3 t

5457

O 0 0 0

1t 1t 1t

1 t

O 0 0 0

1t 1t

1 t 1t

H32 0 0 1

1 t 1t 1t 1t

H34 0 1t

1 t

2t 2t

2 t 2t

5652

H36 1t 1t

1 t 2t

3 t

4 t

H38 1t

1 t 2t

3t 4t 5t

5 t 6t

H25 0 0 0 1t … … … …

5657

H28 1t

1 t 2t

3t … … … …

O 0 0 0 1t 1t 1t

1 t

T4 0 0 1t

1 t, 2 t 2t

3 t

6061

(b)

T6 1t 1t

1 t 2t

3 t 4t

O 0 0 … … … … … …

H12 0 0 … … … … … …

H14 0 0 … … … … … …

H16 0

… … … … … …

7072

H18 1t 1t … … … … … …

O 0 0 1t 1t

1 t 2t 3t

7075

(b)

T6 3t 4t 5t 6t 6t 8t 9t

9 t

O 0 0 1t

1 t 1t 2t 3t

7178

(b)

T6 3t 4t 5t 6t 6t 8t 9t

9 t

(a) The radii listed are the minimum recommended for bending sheets and plates without fracturing in a

standard press brake with air bend dies. Other bending operations may require larger radii or permit smaller

radii. The minimum permissible radii also vary with the design and condition of the tooling.

(b) Tempers T361 and T861 formerly designated T36 and T86, respectively.

tempers of the bare alloy.

Table 2 Maximum thicknesses of aluminum alloy sheet that can be cold bent 180° over

zero radius

Maximum sheet thickness Alloy Temper

mm in.

O 3.2

H12 1.6

H14 1.6

1100

H16 0.4

Alclad 2014

O 1.6

2024

O 1.6

O 3.2

H12 1.6

3003

H14 1.6

O 3.2

H32 0.8

3004

H34 0.4

O 3.2

H12 1.6

H14 1.6

5005

H32 3.2

H34 0.8

O 3.2

H32 1.6

5050

H34 0.8

O 3.2

H32 0.8

5052

H34 0.4

5086

O 3.2

O 1.6

5154

H32 0.8

O 3.2

5457

H25 0.8

O 1.6

6061

T4 0.8

7075

O 0.8

Table 3 Minimum bend radii for 1008 or 1010 steel sheet

Minimum bend radius Quality

or temper

Parallel to rolling

direction

Across rolling

direction

Cold rolled

Commercial

0.25 mm (0.01 in.)

Drawing, rimmed

0.25 mm (0.01 in.)

Drawing, killed

0.25 mm (0.01 in.)

Enameling

0.25 mm (0.01 in.)

Cold rolled, special properties

Quarter hard

(a)

Half hard

(b)

NR 1t

Full hard

(c)

NR NR

Hot rolled

Commercial

Up to 2.3 mm (0.090 in.)

More than 2.3 mm (0.090 in.)

1– t

Drawing

Up to 2.3 mm (0.090 in.)

t t

More than 2.3 mm (0.090 in.)

(a) Note: t, sheet thickness; NR, not recommended.

(b) 60–75 HRB.

(d) 84 HRB min

Table 4 Typical bending limits for six commonly formed stainless steels

Minimum bend radius

Quarter hard, cold rolled

Type

Annealed to

4.7 mm

(0.187 in.)

thick

(180° bend)

1.27 mm

(0.050 in.)

thick

(180° bend)

1.3 to 4.7 mm

(0.051 to

0.187 in.)

thick

(90° bend)

301, 302, 304

t t

316

1t 1t

410, 430

1t … …

Note: t, stock thickness

Introduction to Hardness Testing

Gopal Revankar, Deere & Company

Introduction

THE TERM HARDNESS, as it is used in industry, may be defined as the ability of a material to resist

permanent indentation or deformation when in contact with an indenter under load. Generally a hardness test

consists of pressing an indenter of known geometry and mechanical properties into the test material. The

hardness of the material is quantified using one of a variety of scales that directly or indirectly indicate the

contact pressure involved in deforming the test surface. Since the indenter is pressed into the material during

testing, hardness is also viewed as the ability of a material to resist compressive loads. The indenter may be

spherical (Brinell test), pyramidal (Vickers and Knoop tests), or conical (Rockwell test). In the Brinell, Vickers,

and Knoop tests, hardness value is the load supported by unit area of the indentation, expressed in kilograms

per square millimeter (kgf/mm

). In the Rockwell tests, the depth of indentation at a prescribed load is

determined and converted to a hardness number (without measurement units), which is inversely related to the

depth.

Hardness tests are no longer limited to metals, and the currently available tools and procedures cover a vast

range of materials including polymers, elastomers, thin films, semiconductors, and ceramics. Hardness

measurements as applied to specific classes of materials convey different fundamental aspects of the material.

Thus, for metals, hardness is directly proportional to the uniaxial yield stress at the strain imposed by the

indentation. This statement, however, may not apply in the case of polymers, since their yield stress is ill

defined. Yet hardness measurement may be a useful characterization technique for different properties of

polymers, such as storage and loss modulus. Similarly, the measured hardness of ceramics and glasses may

relate to their fracture toughness, and there appears to be some correlation between microhardness and

compressive strength (Ref 1).

The consequence of material hardness also depends on its application in industry. For example, a fracture

mechanics engineer may consider a hard material as brittle and less reliable under impact loads; a tribologist

may consider high hardness as desirable to reduce plastic deformation and wear in bearing applications. A

metallurgist would like to have lower hardness for cold rolling of metals, and a manufacturing engineer would

prefer less hard materials for easy and faster machining and increased production. These considerations lead,

during component design, to the selection of different types of materials and manufacturing processes to obtain

the required material properties of the final product, which are, in many cases, estimated by measuring the

hardness of the material.

Hardness, though apparently simple in concept, is a property that represents an effect of complex elastic and

plastic stress fields set up in the material being tested. The microscopic events such as dislocation movements

and phase transformations that may occur in a material under the indenter should not be expected to exactly

repeat themselves for every indentation, even under identical test conditions. Yet experience has shown that the

indentations produced under the same test conditions are macroscopically nearly identical, and measurements

of their dimensions yield fairly repeatable hardness numbers for a given material. This observation by James A.

Brinell in the case of a spherical indenter led to the introduction of the Brinell hardness test (Ref 2). This was

followed by other tests (already mentioned) with unique advantages over the Brinell indenter, as described in

the various articles of this Section.

Hardness testing is perhaps the simplest and the least expensive method of mechanically characterizing a

material since it does not require an elaborate specimen preparation, involves rather inexpensive testing

equipment, and is relatively quick. The theoretical and empirical investigations have resulted in fairly accurate

quantitative relationships between hardness and other mechanical properties of materials such as ultimate

tensile strength, yield strength and strain hardening coefficient (Ref 3, 4), and fatigue strength and creep (Ref

5). These relationships help measure these properties with an accuracy sufficient for quality control during the

intermediate and final stages of manufacturing. Many times hardness testing is the only nondestructive test

alternative available to qualify and release finished components for end application.

References cited in this section

1. R.W. Rice, The Compressive Strength of Ceramics in Materials Science Research, Vol 5, Ceramics in

Severe Environments, W.W. Kriegel and H. Palmour III, Ed., Plenum, 1971, p 195–229

2. J.A. Brinell, II Cong. Int. Méthodes d' Essai (Paris), 1900

3. M.O. Lai and K.B. Lim, J. of Mater. Sci., Vol 26 (1991), p 2031–2036

4. S.C. Chang, M.T. Jahn, C.M. Wan, J.Y.M. Wan, and T.K. Hsu, J. Mater. Sci., Vol 11, 1976, p 623

5. W. Kohlhöfer and R.K. Penny, Int. J. Pressure Vessels Piping, Vol 61, 1995, p 65–75

Introduction to Hardness Testing

Gopal Revankar, Deere & Company

Principles of Hardness Testing (Ref 6)

Brinell versus Meyer Hardness. In the Brinell hardness test, a hard spherical indenter is pressed under a fixed

normal load onto the smooth surface of a material. When the equilibrium is reached, the load and the indenter

are withdrawn, and the diameter of the indentation formed on the surface is measured using a microscope with

a built-in millimeter scale. The Brinell hardness is expressed as the ratio of the indenter load W to the area of

the concave (i.e., contact) surface of the spherical indentation that is assumed to support the load and is given as

Brinell hardness number (BHN) denoted by HB. Thus:

(Eq 1)

where W is the load in kilograms, and d and D are the diameters of the indentation and the indenter,

respectively, in millimeters.

However, BHN, though widely and universally accepted in manufacturing practice, is not considered a

satisfactory concept, since it does not represent the mean pressure over the curved area (see the following

discussion). Consideration of equilibrium of the indenter (sphere) under load would show (Ref 6) that the mean

pressure over the indentation spherical area is given by load divided by the projected area of indentation, or:

P = W/(πd

/ 4)

(Eq 2)

where P is the Meyer hardness (Ref 7), also expressed in kilograms per square millimeter (kgf/mm

). A more

fundamental relationship between the load and the indentation diameter is given by Meyer's law, which states

that:

W = cd

(Eq 3)

where c and n are constants for a given material. The value of n generally varies between 2 and 2.5; it is

approximately 2.6 for fully annealed metals and approximately 2.0 for fully cold worked metals. It may be

mentioned here that fully annealed metals tend to work harden whereas the highly cold worked metals have a

near ideal plastic behavior; that is, they do not work harden.

If D

, D

, … are the diameters of the indenters producing indentations of diameters d

, d

, … produced

by the same load, then Meyer's law states that:

W = = = =…

(Eq 4)

Meyer determined experimentally that, for a given material, the value of n is almost independent of D, and that

c and D are inversely related such that:

A = c

n-2

= c

n-2

= c

n-2

…= constant

Equation 4 then becomes:

W = / = /

= / …

(Eq 5)

This relationship may be expressed in two useful forms:

W/d

= A(d/D)

n-2

(Eq 6)

and

W/D

= A (d/D)

(Eq 7)

where A is a constant.

Equation 6 shows that, for geometrically similar indentations (see Fig. 1) for which d/D is fixed, the ratio W/d

and, hence, Meyer hardness, which is proportional to this ratio, will be constant. Similarly, the Brinell hardness

values, which are related to Meyer hardness through a constant, will also be constant. According to Eq 7, the

indentations produced by using different values of W and D will be geometrically similar (i.e., d/D = a constant)

and will give the same hardness values if the ratio W/D

is held constant. This concept is used in practical

hardness measurements when the load, and, hence, D, need to be varied depending on the type of material and

the shape and size of the component. Thus hardness values obtained using a 3000 kg load and 10 mm diameter

ball would be practically the same as when a 750 kg load and a 5 mm diameter ball are used, since W/D

= 30

in both cases.

Fig. 1 Geometrically similar indentations produced by spherical indenters of different diameters. Note

that the solid angle φ and the ratio d/D are the same for both the indentations

In the case of highly cold worked metals, it is experimentally observed that Meyer hardness is independent of

the applied load; that is, the mean pressure resisting deformation is approximately constant. Brinell hardness,

however, is nearly constant at smaller loads but decreases as the load is increased, indicating incorrectly that the

materials soften at higher indentation loads. Similarly, for fully annealed metals (which undergo work

hardening during the indentation process), Meyer hardness is found to increase steadily with load, suggesting

the presence of work hardening. Brinell hardness would, however, rise at first and then fall as the load

increases, again suggesting material softening. Meyer hardness, which is an expression of the mean yield

pressure, is therefore considered a more appropriate and satisfactory measure of resistance to indentation (see

also further discussion that follows and “Summary” in this article).

Plastic Deformation of Ideal Plastic Metals under an Indenter. The complex stresses set up in a material due to

indentation and immediately next to the indenter can be resolved into three principal stresses, p

, p

, and p

, and

it has been shown empirically that, for the onset of plastic deformation:

[(p

- p

)

+ (p

- p

)

+ (p

- p

)

] = constant

(Eq 8)

For uniaxial stresses as in a tensile test, p

= p

= 0 and p

= Y at the onset of yielding, where Y is the yield

stress. Equation 8 gives:

⅓(2 ) = ⅓(2Y

) = constant

This leads to the equation:

- p

)

+ (p

- p

)

+ (p

- p

)

= 2Y

(Eq 9)

which is the Huber-Mises criterion for the onset of plasticity.

An alternative criterion, due to Tresca and Mohr, is based on the assumption that plastic deformation occurs

under the action of three principle stresses, p

> p

, when the maximum shear stress, ½(p

- p

), exceeds a

critical value. The value of this stress can be obtained, again, by considering uniaxial loading with p

= p

= 0,

when the maximum shear stress is ½p

. Since p

= Y at yielding:

½(p

- p

) = ½Y or

- p

= Y, when p

> p

(Eq 10)

It may be shown for a two dimensional plastic flow, that is, under plane strain conditions of deformation, that p

= (p

+ p

), with zero strain in the direction of p

. Substituting this in Eq 9 yields:

- p

= (2/ )Y

(Eq 11)

Thus, according to the Huber-Mises criterion, the plasticity under the indenter occurs when (p

- p

) reaches the

value (2/ ) Y (or 1.15 Y), which is 15% higher than that for Tresca or Mohr criterion.

When plastic strain occurs in a plane (plane strain), the system of stresses can be represented by the sum of a

hydrostatic pressure, p, and a maximum shear stress, k, where 2k = 1.15 Y or Y (depending on the criterion

chosen) at every point in the plastically deformed region of the material. Since the hydrostatic component does

not produce deformation, only the shear stress may be considered responsible for the plastic strain. The stress

field in the deformed material volume may therefore be represented by the maximum shear stresses in the form

of slip lines (see Fig. 2). These lines should not be confused with the slip lines associated with dislocation

movements under the action of stresses, which appear on the metal surface, or the dislocation images observed

as lines in transmission electron microscopy.

Fig. 2 Slip-line field solutions for a flat-ended, two-dimensional punch having a width 2a. (a) Prandtl's

flow pattern. Flow in the center area is downward and to the left and right, as indicated by arrows in the

adjoining areas. (b) Hill's flow pattern. Flow is to left and right in directions indicated by arrows in (a),

but is separated. The dashed line AFE has been added to 3(a) to approximately suggest areas of elastic-

plastic and elastic strain regions. Strain between ABCDE and AFE is partly plastic and partly elastic,

and that below AFE is mostly elastic. Source: Ref 6

Deformation of an Ideal Plastic Metal by a Flat Punch (Two Dimensional Deformation). The rigorous solutions

for the problem of plastic indentation have been possible only for the case of a two-dimensional deformation.

When a load is first applied to an infinitely long and rigid punch with uniform width and negligible thickness,

the shear stresses in an ideal plastic metal at the punch edges A and B (Fig. 3) will be very high, and these

points will reach a plasticity state much earlier than the rest of the contact length. As the load is increased, the

plasticity region expands outward from these edges until it covers the whole width of the punch. The pressure

on the punch face at this state of plastic deformation was first derived by Prandtl (Ref 8) and later by Hill (Ref

9) through the slip line analysis already mentioned, and the corresponding slip line patterns are shown in Fig. 2.

Fig. 3 Two-dimensional deformation (plain strain) of an ideal plastic semi-infinite metal by a rigid flat

punch of width 2a. The onset of plasticity occurs at the edges A and B. Source: Ref 6

The slip line analysis of plastic deformation shows that the mean normal pressure, P

, on the punch is given by:

= 2k(1 + ½π)

(Eq 12)

where k is the magnitude of maximum shear stress, equal to Y/2 if Tresca or Mohr criterion is used and

(1.15Y)/2 if Huber-Mises criterion is used. The Tresca or Mohr criterion holds for fully annealed mild steel,

whereas the Huber-Mises criterion is applicable to most other metals. The mean pressure on the punch,

therefore, would be between 2.6Y and 3.0Y. The shaded region in Fig. 2(b) represents the volume of plastic

deformation where elastic strains may be neglected, and the region between ABCDE and AFE may be

considered to have both plastic and elastic deformation. The volume below AFE may be considered a region of

totally elastic strain.

An approximate extension of the above analysis for a two-dimensional flat punch to the case of a three-

dimensional circular punch has shown that the pressure is not uniform over the area of the circular punch (as it

is slightly higher at the center than at the edges) and that the mean pressure, P

, over the face of the punch

when the material under the punch is plastically deformed is still given by the same relationship, P

≈ 3Y. Note

that P

is a quantity similar to Meyer hardness discussed previously.

Deformation of Ideal Plastic Metal by Spherical Indenters. The preceding analysis of plastic deformation under

the flat and circular punches may now be used to understand the stress field under a spherical indenter pressed

into the surface of an ideal plastic metal.

Based on Tresca or Huber-Mises criterion, Timoshenko (Ref 10) showed that when a sphere is pressed into a

metal under load, the maximum shear stress and, hence, the plastic deformation starts at a depth equal to 0.5a

where 2a is the indentation diameter, as at X in Fig. 4. The maximum shear stress at this point has been shown

to be 0.47 P

where P

is the mean pressure on the indenter. From Tresca-Mohr criterion, it is obvious, the

plastic transformation would start at X when 0.47 P

= ½Y, or P

= 1.1Y. Figure 4 also shows contours (Ref 11)

of shear stress expressed in terms of P

as a function of the distance from X.