Stress and strain are closely related, but they describe different parts of a material’s response to load. Stress shows the internal force acting within a material, while strain shows the resulting deformation. Understanding both helps engineers predict whether a part will remain stable, deform permanently, or lose its intended function under load.
This guide explains stress, strain, their key differences, relationship, and the stress-strain curve. It also connects these concepts to engineering materials, material selection, part geometry, dimensional stability, and practical part design.
What Is Stress in Engineering?
Stress is the internal force per unit area that develops within a material when an external load acts on it. It describes the intensity of the internal force acting across a given cross-section. The SI unit of stress is the pascal (Pa), where 1 Pa = 1 N/m². In mechanical engineering, stress is commonly expressed in megapascals (MPa), and 1 MPa = 1 N/mm².
For a simple axial load, normal stress is calculated as:
σ = F / A
Where:
- σ = normal stress
- F = applied force
- A = cross-sectional area
For example, if a tensile force of 10,000 N acts on a cross-sectional area of 100 mm²: σ = 10,000 N / 100 mm² = 100 MPa
This value shows the intensity of the load within that section. Engineers can compare it with relevant material properties, such as yield strength, to judge whether the material can carry the load without permanent deformation.
Common Types of Stress
Mechanical parts can experience several types of stress depending on the direction and nature of the applied load. Some components carry one dominant stress type, while others experience several at the same time.
- Tensile stress: A pulling force stretches the material. Tie rods, bolts under tension, and loaded bracket arms can experience tensile stress.
- Compressive stress: A pushing force shortens or compresses the material. Spacers, supports, press components, and clamped sections often carry compressive loads.
- Shear stress: Forces act parallel to a cross section and try to slide one part of the material past another. Pins, bolts, keys, and some fastener joints commonly experience shear.
- Bending stress: A bending load creates tension on one side of a section and compression on the opposite side. Brackets, levers, shafts, and mounting plates often experience this stress pattern.
- Torsional stress: Torque twists a component and creates shear stress across its section. Drive shafts, spindles, couplings, and rotating transmission parts commonly experience torsion.
What Is Strain in Engineering?
Strain is the deformation of a material relative to its original size or shape when a load is applied. It describes how much the material stretches, compresses, or changes shape compared with its initial condition. Strain is dimensionless because it is expressed as a ratio between the change in dimension and the original dimension. It therefore represents relative deformation rather than an absolute change in size. This distinction becomes important when comparing parts of different sizes or materials with different stiffness.
For axial loading, engineering strain is expressed as:
ε = ΔL / L₀
Where:
- ε = engineering strain
- ΔL = change in length
- L₀ = original length
If a 100 mm section stretches to 100.2 mm, its change in length is 0.2 mm. The resulting strain is: ε = 0.2 / 100 = 0.002, or 0.2%. This means the section has elongated by 0.2% relative to its original length.
Common Types of Strain
Strain takes different forms depending on the direction of deformation and the loading condition. A component may experience one dominant strain mode or a combination of several modes during service. The main strain types used in mechanical analysis include:
- Tensile strain: Elongation occurs along the direction of a tensile load.
- Compressive strain: A compressive load reduces the material’s length along the loading direction.
- Shear strain: Angular distortion develops when one section shifts relative to another.
- Volumetric strain: The overall volume changes relative to its original volume under loading.
Stress vs Strain: What Are the Key Differences?
The main difference between stress and strain is that stress refers to the internal force acting within a material, while strain measures the deformation caused by that loading. Stress therefore relates to the intensity of loading within a part, whereas strain relates to the amount of stretching, compression, or distortion compared with the original dimensions.
The two also differ in measurement and design meaning. Stress has units such as Pa or MPa, while strain is dimensionless. More importantly, the same stress can produce different amounts of strain in different materials because their stiffness is not the same. This is why engineers consider both values when evaluating whether a part can carry a load and still maintain its required shape and dimensions.
| Aspect | Stress | Strain |
| Definition | Internal force per unit area | Deformation relative to the original dimension |
| Indicates | Intensity of internal loading | Amount of relative deformation |
| Symbol | σ for normal stress; τ for shear stress | ε for normal strain; γ for shear strain |
| Basic formula | σ = F / A | ε = ΔL / L₀ |
| Units | Pa; commonly MPa in mechanical engineering | Dimensionless; often expressed as % |
| Main factors | Applied load and cross-sectional geometry | Stress level, material stiffness, and loading condition |
| Design focus | Strength and load capacity | Deformation and dimensional change |
What Is the Relationship Between Stress and Strain?
The stress-strain relationship shows how a material’s deformation changes as the applied stress increases. Within the linear elastic range, stress and strain are directly proportional according to Hooke’s law, and Young’s modulus defines the proportionality between them. Beyond this range, the relationship becomes nonlinear as the material begins to yield and develop permanent deformation.
Hooke’s law expresses the linear relationship as: σ = Eε
Where:
- σ = stress
- E = Young’s modulus
- ε = strain
This means that increasing stress produces a proportional increase in strain while the material remains within its linear elastic range. For example, doubling the stress will approximately double the strain under the same material conditions.
Young’s modulus can also be expressed as E = σ / ε, which represents the ratio of stress to strain within the linear elastic range. A higher Young’s modulus means that more stress is required to produce the same amount of strain, while a lower modulus means the material deforms more under the same stress. After the material leaves the linear elastic range, stress and strain no longer increase proportionally. The stress-strain curve illustrates this transition into yielding and further deformation.
Understanding the Stress-Strain Curve
A stress-strain curve plots stress on the vertical axis and strain on the horizontal axis as a material is loaded in tension. The curve in the figure represents the typical engineering stress-strain behavior of a ductile metal. Reading it from left to right shows the material moving from elastic deformation to yielding, plastic deformation, maximum tensile stress, necking, and finally fracture.
Elastic Region and Proportional Limit
The curve begins with a nearly straight line. In this linear elastic region, stress increases in direct proportion to strain, following the stress-strain relationship described by Hooke’s law. The deformation that develops in this region is elastic strain, which is recoverable when the load is removed.
The slope of this straight section represents Young’s modulus. A steeper slope indicates greater stiffness because more stress is required to produce the same amount of elastic strain. The proportional limit marks the point where stress and strain begin to deviate from this linear relationship.
For engineering parts, this region is especially important when dimensional stability matters. A component does not need to yield or fracture before deformation becomes a functional problem. Excessive elastic deflection alone can affect alignment, fit, or positioning under load.
Yielding and Plastic Deformation
As loading continues, the material reaches the yield region, where permanent deformation begins. Strain can now increase significantly without the same proportional increase in stress. Removing the load after this stage leaves some permanent strain in the material.
The curve in the figure shows a small drop just after yielding. This type of yield behavior appears clearly in some steels, while materials such as many aluminum alloys show a smoother transition. For materials without a distinct yield point, engineers commonly determine yield strength using a 0.2% offset method.
After yielding, the curve rises again as strain hardening develops. The material continues to deform plastically, but increasing stress is required to produce further strain. This rising section continues until the curve reaches its highest engineering stress.
Ultimate Tensile Strength, Necking, and Fracture
The curve reaches its highest point at the ultimate tensile strength (UTS), which is the maximum engineering stress recorded during the tensile test. Up to this point, deformation remains relatively distributed along the gauge section. UTS marks the transition toward localized deformation in a typical ductile metal.
After UTS, necking begins. Deformation concentrates in a small region of the specimen, causing its cross-sectional area to decrease rapidly. At the same time, the load carried by the specimen begins to fall. Because engineering stress is still calculated using the original cross-sectional area, the engineering stress shown on the curve decreases after UTS.
As necking becomes more severe, the remaining section can no longer sustain the load and fracture occurs. The fracture point marks the end of the tensile test. For most mechanical parts, however, fracture is not the normal design limit; yielding, excessive deformation, fatigue, or buckling may make the part unusable much earlier.
Engineering Stress and Strain vs True Stress and Strain
Engineering stress and strain are calculated from a specimen’s original dimensions. Engineering stress uses the original cross-sectional area, while engineering strain compares the change in length with the original gauge length. In contrast, true stress and strain account for the specimen’s changing geometry during deformation: true stress uses the current cross-sectional area, while true strain reflects deformation relative to the changing length.
At small deformation, the difference between the two is usually minor. As plastic deformation increases, changes in the specimen geometry become larger, so engineering and true values increasingly differ. Engineering stress and strain are commonly used for standard material properties and conventional design, while true stress and strain are more useful when large plastic deformation needs to be represented accurately.
How Does Stress-Strain Behavior Differ Between Engineering Materials?
Different engineering materials produce different stress-strain curves because their stiffness, yield behavior, ductility, and deformation characteristics are not the same. Metals and engineering plastics can therefore show very different amounts of strain under the same stress and very different transitions from elastic to permanent deformation.
Metals
Metals usually show an elastic region followed by yielding and plastic deformation, but the slope and shape of the curve vary by alloy and condition. ASTM E8/E8M-25 provides standardized room-temperature tensile testing for metallic materials and covers properties including yield strength, tensile strength, elongation, and reduction of area. These measured properties help describe where a metal begins to yield, the maximum tensile stress it reaches, and the amount of deformation it can sustain before fracture.
- Steel: Generally has high stiffness and develops relatively little elastic strain under a given stress. Some low-carbon steels show a distinct yield point, while alloy and heat-treated steels may transition more gradually into plastic deformation.
- Aluminum: Has a much lower Young’s modulus than steel, so it develops more elastic strain under the same stress. Most aluminum alloys do not show a sharp yield point, so engineers commonly use a 0.2% offset yield strength.
- Stainless steel: Austenitic grades such as 304 and 316 usually show gradual yielding followed by noticeable strain hardening, allowing substantial plastic deformation before fracture.
- Titanium: Combines relatively high strength with lower stiffness than steel, so a titanium part can remain below its yield strength while showing more elastic deflection than a similarly loaded steel part.
Engineering Plastics
Engineering plastics generally show lower stiffness and more nonlinear stress-strain behavior than metals, so they often develop greater strain under the same applied stress. ASTM D638 and ISO 527 are commonly used to evaluate their tensile properties and stress-strain behavior. Most machinable engineering plastics are thermoplastics, which generally allow more deformation than thermosetting polymers before failure.
- POM: Offers relatively high stiffness and dimensional stability among common engineering plastics, with lower deformation under load than many softer polymers.
- Nylon: Can tolerate substantial strain, but moisture absorption can reduce stiffness and change its dimensional and mechanical response.
- PEEK: Retains relatively high strength and stiffness over a wider temperature range than many engineering plastics, making its stress-strain behavior more stable under elevated-temperature service.
- PTFE: Has low stiffness and develops relatively large strain under modest stress. Long-term loading can also produce significant creep.
Why Do Stress and Strain Matter in Part Design?
Stress and strain provide the basis for key part-design decisions. Engineers use them to select suitable materials, define load-bearing sections, reduce local stress concentrations, and keep deformation within functional limits under service loads.
Material Selection
Material selection should consider both strength and stiffness because they affect stress and strain differently. Yield strength controls resistance to permanent deformation, while Young’s modulus determines elastic strain under load.
A material with higher strength is not necessarily more resistant to elastic deformation. 7075-T6 aluminum is significantly stronger than 6061-T6, but their elastic moduli are similar, so changing between them does not greatly reduce deflection. Steel is considerably stiffer than aluminum, while titanium combines high strength with lower stiffness than steel. Engineering plastics such as POM and PEEK have much lower moduli than metals, so the same stress can produce greater elastic strain and may require a larger section when deformation or alignment must be tightly controlled.
Cross-Section and Wall Thickness
Cross-section and wall thickness directly influence the stress and deformation that develop in a part under load. A larger load-bearing area reduces nominal stress, while greater section depth or thickness increases stiffness and limits elastic deformation. A part can therefore remain below its yield strength but still deform too much to meet its functional requirements.
Increasing the effective load-bearing area helps reduce stress, while greater section depth, thicker critical walls, ribs, and gussets can improve stiffness where deformation becomes the limiting factor. These changes allow engineers to strengthen the required regions without adding unnecessary material throughout the entire part.
Stress Concentration in Part Geometry
Part geometry can create local stresses far above the nominal stress in the surrounding section. Holes, keyways, grooves, shoulders, sharp internal corners, and abrupt thickness changes interrupt the load path and concentrate stress in a small region. These local peaks can cause yielding or fatigue damage even when the average stress remains within the material limit.
Increasing fillet radii, smoothing section transitions, maintaining sufficient material around holes and slots, and avoiding abrupt geometry changes can reduce local stress concentration. Critical features may also require local peak-stress evaluation rather than nominal stress alone, particularly under cyclic or combined loading. For CNC parts, you also need to balance the radius with mating clearance, shoulder function, cutter access, and tool geometry so that the stress-reducing feature remains practical to manufacture.
Dimensional Stability and Tolerance
A part can remain below its yield strength and still deform enough to affect its function. Elastic strain can change clearances, alignment, flatness, or the relative position of critical features while the part is under load, even though the dimensions recover after unloading.
For this reason, designers should define acceptable deformation as well as dimensional tolerance. A bearing bore, mounting surface, shaft support, or mating feature may meet its drawing tolerance when unloaded but move outside its functional position during service. Increasing structural stiffness, improving support, or modifying the load path is usually more effective than simply specifying a tighter machining tolerance when deformation is the underlying problem.
Stress and Strain in Common CNC Machined Parts
Different CNC machined parts show different stress and strain patterns under service loads. Brackets often face bending and local stress around mounting features, shafts and pins carry torsion, bending, or shear, while housings and fixture plates must control deformation to maintain alignment and dimensional accuracy.
Brackets and Mounting Components
Brackets commonly carry bending, tensile, and shear loads between mounting points and the supported component. Bending often produces the greatest strain at unsupported arms or thin sections, while bolt holes and inside corners can develop higher local stresses.
For a mounting bracket, adequate strength alone may not be enough. Excessive elastic deflection can shift the mounted component out of position even when the bracket never yields. Therefore, increasing section depth along the bending direction can improve stiffness efficiently, while generous transition radii and sufficient material around mounting holes help control local peak stress.
Shafts, Pins, and Rotating Components
Shafts often experience torsion and bending at the same time, while pins often carry shear and bearing loads. Torque creates shear stress through the shaft section, and radial loads from gears, pulleys, bearings, or couplings can add bending stress and shaft deflection.
Shoulders, keyways, retaining-ring grooves, and diameter transitions can create local stress concentrations above the nominal shaft stress. For CNC-turned shafts, transition radii should reduce these local peaks without interfering with mating clearance or shoulder function. Excessive elastic strain can also increase shaft deflection or angular misalignment, affecting bearings, seals, gears, and other connected components.
Housings, Plates, and Fixtures
Housings, plates, and fixtures often support bearings, fasteners, or clamped assemblies, so stiffness and deformation control can matter as much as material strength. Clamping forces, bolt preload, bearing loads, and external forces can bend thin walls or plates and distort critical bores or mounting surfaces, even when the material remains below its yield strength.
Wall thickness, rib placement, support spacing, and pocket depth all affect the strain and deflection of these parts under load. When dimensional accuracy is critical, reinforce flexible regions or improve the load path to limit deformation. A fixture plate that flexes during clamping or a housing that distorts around a bearing bore can lose functional accuracy even when its unloaded dimensions meet the drawing tolerance.
Practical Stress and Strain Considerations Before CNC Production
Before CNC production, confirm that the final design still reflects the stress and strain conditions expected in actual service. The review should connect the specified material, critical geometry, allowable deformation, and machining requirements.
- Define the actual load cases: Include tension, compression, bending, shear, torsion, impact, thermal effects, or cyclic loading where they apply. The design should reflect the loads the finished part will actually experience rather than a single simplified load case.
- Use material data for the specified condition: Mechanical properties should match the actual alloy, temper, heat treatment, or polymer grade. A 7075-T6 aluminum part, for example, should not rely on generic aluminum strength data.
- Review critical load-bearing geometry: Check thin sections, reduced diameters, pockets, holes, threads, grooves, shoulders, and section transitions where local stress concentrations or excessive deformation may develop.
- Verify both strength and deformation limits: Confirm that critical sections remain below the required stress limit and that elastic deformation does not exceed functional requirements for alignment, clearance, flatness, or positioning.
- Confirm CNC manufacturability: Fillet radii, thin walls, deep pockets, and other structurally important features should still allow practical machining, inspection, and assembly without compromising their intended mechanical function.
Conclusion
Stress and strain describe two different but closely connected aspects of material behavior: stress represents the internal force per unit area within a material, while strain shows the resulting deformation. Their relationship helps define stiffness, yielding, plastic deformation, and the limits that matter in practical part design.
If you are preparing a load-bearing or dimension-critical CNC part, DZ Making can review your drawing, material specification, tolerances, and key functional requirements before production. Send us your CAD files or drawings for a manufacturability review and CNC machining quote.
FAQs
1. Does stress cause strain?
Yes, mechanical stress normally produces strain in a material. The amount of strain depends on the stress level and the material response. However, strain does not always come from mechanical stress; temperature changes can also cause expansion or contraction, and restraint of that deformation can then generate thermal stress.
2. What is the relationship between stress, strain, and Young’s modulus?
Young’s modulus defines the proportional relationship between stress and strain only within the linear elastic range. The relationship is expressed as σ = Eε. Once the material begins nonlinear or plastic deformation, a single Young’s modulus no longer describes the complete stress-strain response.
3. What is the difference between stress and strength?
Stress is the internal force intensity that actually develops in a loaded part, while strength is a material limit used to judge whether that stress is acceptable. Stress changes with load and geometry; properties such as yield strength and ultimate tensile strength come from the material and its condition.
4. What is the difference between elastic and plastic strain?
Elastic strain disappears after unloading, while plastic strain remains as permanent deformation. Once yielding occurs, the total strain can contain both recoverable elastic strain and permanent plastic strain rather than changing instantly from one type to the other.
5. What is allowable stress in part design?
Allowable stress is the maximum stress a part should carry under its intended working conditions. It is usually set below the material’s yield or strength limit by applying an appropriate safety factor, so the part can operate without permanent deformation or failure.
6. Can two materials have the same stress but different strain?
Yes. The same stress can produce different strain in materials with different stiffness. Within the linear elastic range, strain equals stress divided by Young’s modulus, so a lower-modulus material develops more elastic strain under the same stress.
