Why Do Materials Deform? Visualizing Stress and Strain with MATLAB
When designing bridges or mechanical components, how can we ensure they won’t deform or fail? To answer this, we must first understand the forces at play. Let’s dive into the types of loads first.
Loads are primarily classified into static loads and dynamic loads. First, static loads are forces applied slowly that remain constant over time.
Normal Load: A force acting perpendicular to a surface, such as a book resting on a table.
Shear Load: A force causing layers of a material to slide past one another, like the action of scissors.
In contrast, dynamic loads are forces that vary with time.
Repeated Load: A load applied repeatedly in a single direction, typically varying in magnitude.
Alternating Load: A load that cycles between opposite directions.
Impact Load: A sudden, high-force load applied over a very short period.
Now, let’s look at Stress and Strain. Stress is defined as the force acting per unit area. Essentially, it represents the intensity of the internal force distributed within the material. Strain describes the deformation resulting from that stress. It is defined as the ratio of the change in dimension to the original dimension.
The graph below shows a stress-strain diagram generated from a MATLAB simulation of a mild steel tensile test. Note that the data has been slightly modified for educational purposes to make it easier to understand.
Elastic Region: The initial phase up to the Upper Yield Point. This point is the peak stress before the transition to plastic deformation.
Yield Drop & Plateau Region: After the stress drops to the Lower Yield Point, the Yield Plateau Region begins. Here, strain increases significantly with constant or fluctuating stress.
Strain Hardening Region: Stress begins to rise again until it reaches the peak, known as the Ultimate Tensile Strength (UTS).
Necking Region & Fracture: Beyond the UTS, the material enters the Necking Region, where it deforms under less force until final fracture occurs.
Summary
In conclusion, materials deform because the internal stress caused by external loads exceeds the material's limits. This is why plotting the stress-strain curve is so important—it allows us to make more informed decisions when selecting materials for our structural designs.