🚀 Stress-Strain Calculator & Simulator
- Set Material Properties: Click a preset button (Structural Steel, Aluminum Alloy, Brass) or manually enter the Elastic Modulus (E), Yield Strength (Sy), and Ultimate Tensile Strength (Su) in detail.
- Adjust Specimen Dimensions & Load: Set the initial diameter (d₀) and gauge length (L₀) of the specimen, and adjust the applied tensile load (P).
- Observe Real-Time 2D Tensile Behavior: Watch the 2D animation of the cylindrical tensile specimen stretching as the load increases, and observe necking (localized thinning) and fracture when the critical load is exceeded.
- Monitor Operating Point on the Stress-Strain Curve: Diagnose material rigidity through a cursor indicating the current state (elastic deformation, plastic flow, fracture) on the stress-strain diagram on the right, along with a numerical analysis of the safety factor.
📚 Read Detailed Mechanics of Materials Theory & Stress-Strain Diagram Explanation ▼
1. Definition and Engineering Properties of Stress and Strain
In the mechanics of materials, stress (Stress, σ), which defines the internal resistance of a material when an external force is applied, and strain (Strain, ε), which represents the ratio of deformation caused by the external force, are the most fundamental metrics in structural design.
- Engineering Stress (σ): The applied tensile load
Pdivided by the material's initial pre-deformation cross-sectional areaA_0. (σ = P / A_0) - Engineering Strain (ε): The dimensionless ratio of the change in length
ΔLto the initial gauge lengthL_0. (ε = ΔL / L_0)
In the initial stage of loading, stress and strain are linearly proportional. The constant determining this proportional relation is called the Elastic Modulus (Young's Modulus, E), and this relationship is widely known as Hooke's Law (σ = Eε).
2. Key Regions of the Stress-Strain Diagram
When performing a tensile test and gradually increasing the load, a metallic material deforms through the following four behavioral regions:
- Elastic Region: The region where the material returns to its original state once the load is removed. This lies within the proportional limit and elastic limit where Hooke's Law strictly applies.
- Yielding Region (Yield Point / Plastic Flow): The onset of plastic deformation, where strain increases rapidly even with a minute increase in stress. The 0.2% offset yield strength (
Sy) serves as a representative safety criterion. - Plastic/Tensile Region (Ultimate Tensile Strength / UTS): The interval where permanent deformation propagates up to the maximum stress point (
Su) that the material can withstand. - Necking & Fracture: After reaching ultimate strength, localized cross-sectional reduction (necking) at the center of the specimen becomes extreme, causing stress to drop rapidly, eventually leading to fracture (splitting into two pieces).
3. Allowable Load Based on Structural Material Design Standards and Allowable Stress
When performing engineering structural design, to prevent mechanical failure, the yield strength (Sy) of the material is taken as the design reference strength, and the allowable stress (σ_allow) is calculated by applying a safety factor (FS), which is an engineering margin of safety.
σ_allow = Sy / FS → P_allow = σ_allow × A₀ [N]
For steel materials, a safety factor of 1.5 to 2.0 under static loads is typically adopted for design. Under dynamic environments where vibration or cyclic loads act, conservative guidelines of 3.0 to 5.0 or higher are applied to prevent brittle fracture in advance.