**Water**

——

N/A

**Air**

——

N/A

**Ice**

——

2 MPa

**Glass**

——

7 MPa

**Boron carbide**

——

500 MPa

**Graphite**

——

14 MPa

**Carbon fiber**

——

4000 MPa

**Polyethylene**

——

30 MPa

**Polypropylene**

——

27 MPa

**Carbon dioxide**

——

N/A

**Brick**

——

2.8 MPa

**Porcelain**

——

29 MPa

**Tungsten carbide**

——

370 MPa

**Diamond**

——

N/A

**Graphene**

——

130000 MPa

**PET**

——

150 MPa

**Polycarbonate**

——

60 MPa

**Carbon monoxide**

——

N/A

**Sand**

——

N/A

**Limestone**

——

2.5 MPa

**Elektron 21**

——

280 MPa

**Duralumin**

——

450 MPa

**Zirconium-tin alloy**

——

514 MPa

**Austenitic stainless steel**

——

515 MPa

**Mild steel**

——

400-550 MPa

**Gray iron**

——

295 MPa

**TZM alloy**

——

800 MPa

**Inconel**

——

1200 MPa

**ETP**

——

250 MPa

**Cupronickel**

——

275 MPa

**Zamak 3**

——

268 MPa

**Ruby**

——

2100 MPa (compressive)

**Uranium dioxide**

——

N/A

**Polystyrene**

——

48 MPa

**Polyvinyl chloride**

——

48 MPa

**Nitrous oxide**

——

N/A

**Concrete**

——

2 MPa

**Granite**

——

4.8 MPa

**Pure titanium**

——

293 MPa

**6061 alloy**

——

290 MPa

**Zirconium-niobium alloy**

——

514 MPa

**Martensitic stainless steel**

——

760 MPa

**High-carbon steel**

——

685 MPa

**White iron**

——

350 MPa

**Mo-25 Re alloy**

——

1100 MPa

**Hastelloy**

——

600 MPa

**Brass**

——

315 MPa

**Aluminium bronze**

——

550 MPa

**Soft tin solder**

——

56 MPa (19°C)

**Salt**

——

1.65 MPa

**Kevlar**

——

3600 MPa

**Polyamide-Nylon**

——

40 MPa

**Rubber**

——

5 MPa

**Methan**

——

N/A

**Stone wool**

——

0.02 MPa

**Quartz**

——

48 MPa

**Ti-6Al-4V**

——

1170 MPa

**7068 alloy**

——

640 MPa

**Chromoly steel**

——

700 MPa

**Duplex stainless steel**

——

620 MPa

**Tool steel**

——

1860 MPa

**Ductile iron**

——

414 MPa (>60 ksi)

**Tungsten-rhenium alloy**

——

2100 MPa

**Stellite**

——

1200 MPa

**Bronze**

——

310 MPa

**Beryllium copper**

——

1110 MPa

**Amalgam**

——

70 MPa

**Sugar**

——

N/A

**Wax**

——

0.9 MPa

**Coal**

——

20 MPa

**Asphalt concrete**

——

1.2 MPa

**Propane**

——

N/A

**Glass wool**

——

0.02 MPa

**Aerogel**

——

0.08 MPa

**Rose gold**

——

550 MPa

**Yellow gold**

——

300 MPa

**White gold**

——

350 MPa

**PH stainless steel**

——

1000 MPa

**High-speed steel**

——

1200 MPa

**Malleable iron**

——

580 MPa

**Pure tungsten**

——

980 MPa

**Invar**

——

445 MPa

**Constantan**

——

420 MPa

**Nickel silver**

——

400 MPa

**Galistan**

——

N/A

**Oak wood**

——

70 MPa

**Pine wood**

——

35 MPa

**Gasoline**

——

N/A

**Diesel fuel**

——

N/A

**Acetylene**

——

N/A

## Strength of Materials

**Strength of materials** basically considers the relationship between the **external loads** applied to a material and the resulting **deformation** or change in material dimensions. In designing structures and machines, it is important to consider these factors, in order that the material selected will have adequate strength to resist applied loads or forces and retain its original shape. **Strength of a material** is its ability to withstand this applied load without failure or plastic deformation.

However, we must note that the load which will deform a small component, will be less than the load to deform a larger component of the same material. Therefore, the** load (force) is not a suitable term** to describe **strength**. Instead, we can use the **force (load) per unit of area** (σ = F/A), called **stress**, which is constant (until deformation occurs) for a given material regardless of size of the component part. In this concept,** strain** is also very important variable, since it defines the deformation of an object. In summary, the mechanical behavior of solids is usually defined by constitutive **stress-strain relations.** A deformation is called elastic deformation, if the stress is a linear function of strain. In other words, stress and strain follows **Hooke’s law**. Beyond the linear region, stress and strain show nonlinear behavior. This inelastic behavior is called plastic deformation.

A schematic diagram for the **stress-strain curve** of low carbon steel at room temperature is shown in the figure. There are several stages showing different behaviors, which suggests different mechanical properties. To clarify, materials can miss one or more stages shown in the figure, or have totally different stages. In this case we have to distinguish between stress-strain characteristics of **ductile** and **brittle** materials. The following points describe the different regions of the stress-strain curve and the importance of several specific locations.

**Proportional limit**. The proportional limit corresponds to the location of stress at the end of the**linear region**, so the stress-strain graph is a straight line, and the gradient will be equal to the**elastic modulus**of the material. For tensile and compressive stress, the slope of the portion of the curve where stress is proportional to strain is referred to as**Young’s modulus**and**Hooke’s Law**applies. Between the proportional limit and the yield point the Hooke’s Law becomes questionable between and strain increases more rapidly.**Yield point**. The yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning plastic behavior.**Yield strength**or yield stress is the material property defined as the stress at which a material begins to deform plastically whereas yield point is the point where nonlinear (elastic + plastic) deformation begins. Prior to the yield point, the material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible. Some steels and other materials exhibit a behaviour termed a yield point phenomenon. Yield strengths vary from 35 MPa for a low-strength aluminum to greater than 1400 MPa for very high-strength steels.**Ultimate tensile strength**. The**ultimate tensile strength**is the maximum on the engineering stress-strain curve. This corresponds to the**maximum stress**that can be sustained by a structure in tension. Ultimate tensile strength is often shortened to “tensile strength” or even to “the ultimate.” If this stress is applied and maintained, fracture will result. Often, this value is significantly more than the yield stress (as much as 50 to 60 percent more than the yield for some types of metals). When a ductile material reaches its ultimate strength, it experiences necking where the cross-sectional area reduces locally. The stress-strain curve contains no higher stress than the ultimate strength. Even though deformations can continue to increase, the stress usually decreases after the ultimate strength has been achieved. It is an intensive property; therefore its value does not depend on the size of the test specimen. However, it is dependent on other factors, such as the preparation of the specimen, the presence or otherwise of surface defects, and the**temperature**of the test environment and material.**Ultimate tensile strengths**vary from 50 MPa for an aluminum to as high as 3000 MPa for very high-strength steels.**Fracture point**: The**fracture point**is the point of strain where the material physically separates. At this point, the strain reaches its maximum value and the material actually fractures, even though the corresponding stress may be less than the ultimate strength at this point. Ductile materials have a fracture strength lower than the ultimate tensile strength (UTS), whereas in brittle materials the fracture strength is equivalent to the UTS. If a ductile material reaches its ultimate tensile strength in a load-controlled situation, it will continue to deform, with no additional load application, until it ruptures. However, if the loading is displacement-controlled, the deformation of the material may relieve the load, preventing rupture.

In many situations, the yield strength is used to identify the allowable stress to which a material can be subjected. For components that have to withstand high pressures, such as those used in pressurized water reactors (PWRs), this criterion is not adequate. To cover these situations, the **maximum shear stress theory** of failure has been incorporated into the ASME (The American Society of Mechanical Engineers) Boiler and Pressure Vessel Code, Section III, Rules for Construction of Nuclear Pressure Vessels. This theory states that failure of a piping component occurs when the maximum shear stress exceeds the shear stress at the yield point in a tensile test.