Tangeton said:
There is an engineering stress strain curve and a true stress strain curve. The engineering stress strain curve assumes that the member cross section area remains constant at all levels of tensile load, but in actuality, cross section starts to significantly reduce (called necking) at high stress values beyond the yield point, in which case if you plot true stress, which accounts for the reduced cross section area , versus strain, the true stress value always increases up to rupture, whereas if you use engineering stress, you get a peak on the curve prior to significant necking, and beyond that, the stress gets lower because it is assumed that cross section remains constant . The value of the engineering stress at this peak is called the ultimate tensile strength, whereas the breaking strength is the rupture stress at point of failure .
There is an engineering stress strain curve and a true stress strain curve. The engineering stress strain curve assumes that the member cross section area remains constant at all levels of tensile load, but in actuality, cross section starts to significantly reduce (called necking) at high stress values beyond the yield point, in which case if you plot true stress, which accounts for the reduced cross section area , versus strain, the true stress value always increases up to rupture, whereas if you use engineering stress, you get a peak on the curve prior to significant necking, and beyond that, the stress gets lower because it is assumed that cross section remains constant . The value of the engineering stress at this peak is called the ultimate tensile strength, whereas the breaking strength is the rupture stress at point of failure .
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Two vises apply tension to a specimen by pulling at it, stretching the specimen until it fractures. The maximum stress it withstands before fracturing is its ultimate tensile strength.
Ultimate tensile strength (UTS), often shortened to tensile strength (TS), ultimate strength, or F tu {displaystyle F_{text{tu}}} 
The ultimate tensile strength is usually found by performing a tensile test and recording the engineering stress versus strain. The highest point of the stress–strain curve is the ultimate tensile strength and has units of stress. The equivalent point for the case of compression, instead of tension, is called the compressive strength.
Tensile strengths are rarely of any consequence in the design of ductile members, but they are important with brittle members. They are tabulated for common materials such as alloys, composite materials, ceramics, plastics, and wood.
Definition
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The ultimate tensile strength of a material is an intensive property; therefore its value does not depend on the size of the test specimen. However, depending on the material, it may be 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.
Some materials break very sharply, without plastic deformation, in what is called a brittle failure. Others, which are more ductile, including most metals, experience some plastic deformation and possibly necking before fracture.
Tensile strength is defined as a stress, which is measured as force per unit area. For some non-homogeneous materials (or for assembled components) it can be reported just as a force or as a force per unit width. In the International System of Units (SI), the unit is the pascal (Pa) (or a multiple thereof, often megapascals (MPa), using the SI prefix mega); or, equivalently to pascals, newtons per square metre (N/m2). A United States customary unit is pounds per square inch (lb/in2 or psi). Kilopounds per square inch (ksi, or sometimes kpsi) is equal to 1000 psi, and is commonly used in the United States, when measuring tensile strengths.
Ductile materials
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- Ultimate strength
- Yield strength
- Proportional limit stress
- Fracture
- Offset strain (typically 0.2%)
Figure 1: “Engineering” stress–strain (σ–ε) curve typical of aluminum
Many materials can display linear elastic behavior, defined by a linear stress–strain relationship, as shown in figure 1 up to point 3. The elastic behavior of materials often extends into a non-linear region, represented in figure 1 by point 2 (the “yield point”), up to which deformations are completely recoverable upon removal of the load; that is, a specimen loaded elastically in tension will elongate, but will return to its original shape and size when unloaded. Beyond this elastic region, for ductile materials, such as steel, deformations are plastic. A plastically deformed specimen does not completely return to its original size and shape when unloaded. For many applications, plastic deformation is unacceptable, and is used as the design limitation.
After the yield point, ductile metals undergo a period of strain hardening, in which the stress increases again with increasing strain, and they begin to neck, as the cross-sectional area of the specimen decreases due to plastic flow. In a sufficiently ductile material, when necking becomes substantial, it causes a reversal of the engineering stress–strain curve (curve A, figure 2); this is because the engineering stress is calculated assuming the original cross-sectional area before necking. The reversal point is the maximum stress on the engineering stress–strain curve, and the engineering stress coordinate of this point is the ultimate tensile strength, given by point 1.
Ultimate tensile strength is not used in the design of ductile static members because design practices dictate the use of the yield stress. It is, however, used for quality control, because of the ease of testing. It is also used to roughly determine material types for unknown samples.[4]
The ultimate tensile strength is a common engineering parameter to design members made of brittle material because such materials have no yield point.[4]
Testing
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Round bar specimen after tensile stress testing
Aluminium tensile test samples after breakage
The “cup” side of the “cup–cone” characteristic failure pattern
Some parts showing the “cup” shape and some showing the “cone” shape
Typically, the testing involves taking a small sample with a fixed cross-sectional area, and then pulling it with a tensometer at a constant strain (change in gauge length divided by initial gauge length) rate until the sample breaks.
When testing some metals, indentation hardness correlates linearly with tensile strength. This important relation permits economically important nondestructive testing of bulk metal deliveries with lightweight, even portable equipment, such as hand-held Rockwell hardness testers.[5] This practical correlation helps quality assurance in metalworking industries to extend well beyond the laboratory and universal testing machines.
Typical tensile strengths
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^a^b[38] The first nanotube ropes (20 mm in length) whose tensile strength was published (in 2000) had a strength of 3.6 GPa.[39] The density depends on the manufacturing method, and the lowest value is 0.037 or 0.55 (solid).[40]^c[41] The value shown in the table, 1000 MPa, is roughly representative of the results from a few studies involving several different species of spider however specific results varied greatly.[42]^d
Typical Properties of annealed elements
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Typical properties for annealed elements[43]ElementYoung’s
modulus
(GPa)Yield strength
(MPa)Ultimate
strength
(MPa)Silicon1075000–9000Tungsten411550550–620Iron21180–100350Titanium120100–225246–370Copper130117210Tantalum186180200Tin479–1415–200Zinc85–105200–400200–400Nickel170140–350140–195Silver83170Gold79100Aluminium7015–2040–50Lead1612
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References
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Further reading
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What Does Breaking Stress Mean?
Breaking stress is the maximum force that can be applied on a cross sectional area of a material in such a way that the material is unable to withstand any additional amount of stress before breaking.
Breaking stress is calculated with the formula:
Breaking Stress = Force / Area
Breaking stress testing for metals determines how much a particular alloy will elongate before it reaches its ultimate tensile strength and how much load a particular piece of metal can accommodate before it loses structural integrity. Therefore, it is a very important concept in material science and for safety considerations.
Breaking stress may also be known as ultimate tensile stress or breaking strength.
🔎 This calculator deals with axial stress. If you’re studying transverse shear, you should look at our shear stress calculator .
This stress calculator will help you solve the problems in mechanics involving stress, strain, and Young’s modulus. In a few simple steps, you will learn the stress vs. strain relationship for any material that remains elastic. We will also teach you how to calculate strain and how to apply the stress equation.
How to calculate strain and stress
Strain is defined as the measure of deformation – a proportion between the change of length and original length of an object. For example, if you take an elastic band and stretch it so that it is twice longer than initially, then the strain will be equal to 1 (100%).
The formula for strain is:
ε=ΔLL1=L2−L1L1varepsilon = frac{Delta L}{L_1} = frac{L_2 – L_1}{L_1}
ε
=
L
1
Δ
L
=
L
1
L
2
−
L
1
L₁ denotes the initial length, L₂ – the final length, and ΔL is the change in length. Note that strain is dimensionless.
Stress, on the other hand, is the measure of pressure that the particles of a material exert on each other. It is defined as the force acting on the object per unit area. It is different from the pressure, though; when calculating stress, the area considered must be so small that the analyzed particles are assumed to be homogeneous. If we take into account a bigger area, the calculated stress is usually the average value.
The stress equation is:
σ=FAsigma = frac{F}{A}
σ
=
A
F
F denotes the force acting on a body and A denotes the area. Units of stress are the same as units of pressure – Pascals (symbol: Pa) or Newtons per squared meter.
Positive stress means that the object is in tension – it “wants” to elongate (elongation Calculator). Negative stress means that it is in compression and “wants” to become shorter.
Do you know?
There are two types of strain — engineering and true strain. Find out more in our true strain calculator
