Hardness testing is one of the oldest and most reliable measures of whether or not a component part has been successfully heat treated. However, it should not be the only test conducted to confirm this is true. One of the most reliable mechanical tests to help us to predict the behavior of a component under various operating conditions is the simple tensile test. Let’s learn more.

The tensile test (Fig. 1) allows us to measure a material’s response to loading and deformation. By measuring the force required to elongate a specimen to its breaking point, material properties can be determined that will allow engineering designers and quality managers to predict how their materials and products will behave in their intended end-use applications.

Examples of products and industries that use tensile testing include fasteners (e.g., bolts, nuts, screws), seat-belt components, and tubing and pipe manufacturers to name a few. Tensile tests can predict pull-off force, peel and tear resistance and adhesion/bond strength. In the test, one end of a specimen is typically clamped in a load frame while the other end is subjected to a controlled displacement or a controlled load. A transducer or servo-drive connected in series with the specimen provides information about the displacement (δ) as a function of the load (P) applied (or vice versa).

## A Little Theory

The concept of stress, strain and strength of materials is at the core of the engineering discipline. Mechanical properties such as yield strength, tensile strength, ductility, toughness, impact resistance, creep resistance, fatigue resistance, stiffness and others all influence the design, fabrication and service life of equipment.

The engineering measures for stress (σe) and strain (εe) are determined from load and deflection readings using the original specimen cross-sectional area (A0) and length (L0). Formulas for these values are given as follows:

σe = P/A0  (1)

εe = δ/L0  (2)

## Stress-Strain Curves

Stress-strain curves (Fig. 2) can then be generated and divided into “regions” that are descriptive of what is happening on the microscopic level, namely:

A.  Elastic region

B.  Plastic region

1.   Yielding

2.   Strain hardening

3.   Necking

C.  Failure (fracture)

The shape and magnitude of the stress-strain curve of a metal (Fig. 3) will depend on its composition, heat treatment, prior history of plastic deformation and strain rate, temperature, and state of stress imposed during the testing. The parameters that are used to describe the stress-strain curve of a metal are the tensile strength, yield strength or yield point, percent elongation, and reduction of area. The first two are strength parameters, and the last two indicate ductility.

In the early (low strain) portion of the curve, many materials obey Hooke’s law, which states that the deformation is, within a reasonable approximation, linearly proportional to the stress. As a result, the stress is proportional to strain with the constant of proportionality being the modulus of elasticity (i.e. Young’s modulus).

As strain is increased, many materials eventually deviate from this linear proportionality. The point of departure is known as the proportional limit. This nonlinearity is usually associated with so-called “plastic” deformation (flow) in the specimen. In this region, the material is undergoing rearrangement of its atoms (being moved to new equilibrium positions). The degree of plastic flow depends on the mobility mechanism, which in metals (i.e. crystalline materials) can arise from dislocation movement. Materials lacking this mobility (e.g., by having microstructural features that block dislocation motion) are usually brittle rather than ductile. The stress-strain curves for brittle materials are typically linear over their full range of strain, eventually fracturing without appreciable plastic flow.

As the plastic deformation continues above the yield strength, the engineering stress reaches a maximum point – the (ultimate) tensile strength (T.S.) of the material. The plastic deformation produces dislocations within the region in the curve between the yield strength and the tensile strength. The increasing dislocation density makes the plastic deformation harder.

This phenomenon is strain hardening, and it is a key factor in shaping the material by cold work. The microstructural rearrangements associated with plastic flow are usually not reversed when the load is removed, so the proportional limit is often the same as or at least close to the material’s elastic limit. Elasticity is the property of complete and immediate recovery from an imposed displacement on release of the load, and the elastic limit is the value of stress at which the material experiences a permanent residual strain that is not lost on unloading.

The strain at failure occurs after the specimen fractures. It is the interaction point of the plastic recovery region in strain axis. It is known as ductility. The ductility is the percent elongation at failure and indicates the general ability of the material to be plastically deformed.

A closely related term is the yield stress (sy) of a material, which is the stress needed to induce plastic deformation. Since it is often difficult to pinpoint the exact stress at which plastic deformation begins, the yield stress is taken to be the stress needed to induce a specified amount of permanent strain, typically 0.2%, the so-called “offset” yield stress.

As most heat treater’s know, for steel, hardness can be used to approximate the tensile strength of the material (Equations 3, 4) where HB is Brinell hardness (3,000 kgf load). This relationship is far from exact, however, and only a tensile test can reveal the true nature of the stress-strain relationship of a material.

(3a) TS(MPa)=3.55•HB(HB≤175)

(3b) TS(psi)=515•HB(HB≤175)

and

(4a) TS(MPa)=3.38•HB(HB>175)

(4b) TS(psi)=490•HB(HB>175)

Finally, recall that toughness measures the ability of a material to absorb energy and withstand shock up to fracture (i.e. the ability to absorb energy in the plastic range). In other words, toughness is the amount of energy per unit volume that a material can absorb before rupture and is represented by the area under the stress-strain curve. For further information, refer to The Heat Treat Doctor columns in Industrial Heating entitled “Toughness” (December 2010) and “Toughness Revised” (March 2011).

## In Layman’s Terms

The stress-strain curve is logically divided into two distinct deformation regions corresponding to elastic deformation and plastic deformation. The elastic deformation is temporary and fully recovered when the load is removed. By contrast, the plastic deformation is permanent and not recovered when the load is removed (even though a small portion of the elastic part in the deformation is recovered).

A simple analogy to explain these concepts is the rubber band. When a rubber band is stretched and then released, we say that it is in the elastic region of the curve if it returns to its original shape. The point at which the force we use is great enough to prevent the rubber band from returning to its original shape is the yield point, beyond which we are in the plastic deformation region. Finally, when we stretch a rubber band beyond the material’s ultimate tensile strength, it snaps and we reach the fracture point.

## Tensile-Testing Standards

There are a number of tensile-testing standards, including:

•   ASTM B913, D76, D1876, D3822, D412, D638, D828, E8

•   BS 5G 178, BS EN 1895

•   ISO 37, 527, 1924, 13934

•   MIL-C-39029, MIL-T-7928 IH

References available online

## References

1. Roylance, David, Stress-Strain Curves, MIT, 2001.

2. Instron (www.instron.com)

3. Dolbow, John. E., The Stress-Strain Curve, Duke University (www.dolbow.cee.duke.edu)

4. Engineering Stress-strain Curve: Part One, Key to Metals (www.keytometals.com),

5. Stress-Strain Relationships, Material Testing Solutions (www.mts.com)

6. Atlas of Stress-Strain Curves, Second Edition, ASM International, 2002.

7. K-Street Studios (www.kstreetstudio.com)

8. Etomia, Molecular Simulations Software (www.etomia.org)

9. Penn State University, Department of Engineering Science and Mechanics (www.esm.psu.edu)