How does tensile strength vary with hardness

Here, a force F is applied to an indenter of area A and the indenter is pushed into the metal a distance d. In this example, slip of the metal is restricted to the motion of five triangular portions near the indenter.

The metal is assumed to be isotropic and that slip occurs at a shear stress assumed to be one-half the yield stress, sy. Figure 1 shows the displacement of each triangle as a function of the indenter displacement, d.

If the work performed by the indenter, Fd , is equated to the work performed by each triangle against the shear stress, the following equality is obtained, where each term represents the product of the number of sliding interfaces, the force and the displacement. A more sophisticated analysis using slip-line field theory yields a value of 2. If the hardness is now measured in terms of the applied force and the area, the relationship between hardness and strength is complete.

Of all the various hardness measures, the Brinell test is perhaps ideal for these property relationships because the values are given in units of mass per area of indentation; i. In most cases, a mm ball is used as the indenter and a mass of kg is applied. It is important to note that most hardness values are quoted in terms of mass and that the mass must be multiplied by an appropriate acceleration to obtain the force in calculating stress.

The downfall of this analysis is that metals work-harden during the indentation and, as a result, the hardness correlates much better with the ultimate tensile strength rather than the yield strength. Here at Smalley, one of the physical properties we measure is the ultimate tensile strength of our alloys so our engineers can design the best possible retaining ring or wave spring for your application needs. It can be measured using a tensile tester.

A tensile tester works by applying a mechanical pulling force to the material. If the ultimate tensile strength is exceeded, necking and fracture occur as shown in Figure 2. Fig 1. Stress-Strain Curve. Curve generated by a tensile tester which shows ultimate tensile strength and point of fracture.

Fig 2. Tensile Tester. Fracture of a material during tensile testing. Hardness refers to the amount of resistance to deformation that material has. In this case, it is best used as a means of statistical process control, to see when and if the process drifts.

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Understanding the mechanical properties of strength vs. These properties are related, but there are very important differences between them:. It can be especially easy to confuse the difference between strength and stiffness.

If a material is stiff, then it must be strong enough to support a large load, right? The answer is a resounding no! The elastic modulus measures the stiffness in a material, but strength is a function of the modulus. The stress-strain curve Figure 1 above is a good way of graphically demonstrating this. The ratio of stress to strain is the elastic modulus—stiffness, but the stress, and only the stress, defines the strength of the material.

Remember, strength measures how much stress the material can handle before permanent deformation or fracture occurs, whereas the stiffness measures the resistance to elastic deformation. Understanding the Concepts of Stress and Strain Stress is an internal force resulting from an applied load; it acts on the cross-section of a mechanical or structural component.

Strain is the change in shape or size of a body that occurs whenever a force is applied. Important Definitions for Strength, Stiffness, and Hardness Here are a few important definitions to keep top of mind:. The strength of a material can refer to yield strength, ultimate strength, or fracture strength.

Tensile strength can be calculated from hardness and is convenient because hardness tests—such as Rockwell—are usually simple to do, inexpensive, and nondestructive. Only a small penetration is performed on the specimen. For many metals, tensile strength increases as hardness increases. A reliable online source is www. The image below is a finite element analysis FEA of a beam subjected to a loading.

Axial loading on a straight member Imagine a metal bar in tension, subjected to an axial load of some value. Key point: Both materials are equally strong, but the metal is stiffer than the polymer. In this case, due to a temperature gradient within the member, the thermal stress induces additional strain to the strain already imposed by forces acting on it. Thermal stress has effects on the strength of materials. Computing thermal stress provides insight to select what values of stiffness and strength are appropriate for your design, assuming the temperature difference is not large enough that it will change the microscopic properties of the material!

In the early stages of your design, such as when constructing the CAD model, determine which components will be critical to your design. Determine which ones will be subjected to impact loadings, uniform loadings, concentrated loads, constant loads, etc. If needed, develop graphical representations of complex dynamical systems using bond graph or block-diagram modeling, and utilize software to model sophisticated systems. Calculate the expected stresses on mechanical components to find out where problems may arise or where forces may seem large.

Consider creep and fatigue variables in subsystems and associated with the environment to which your system will be exposed. Metals, ceramics, polymers, and composites are material types with specific mechanical properties.

Metals exhibit two modes: ductile or brittle.