6.1 Failure Modes and Criteria

Failure Modes

Types of Failure

Each failure mode describes a different way a component can stop doing its job. Recognizing which mode is most likely for a given design scenario is the first step in choosing the right failure theory.

• Yielding occurs when stress exceeds the material's yield strength, causing permanent deformation. The part doesn't break, but it no longer holds its intended shape or tolerances.
• Fracture is the actual separation of material into two or more pieces. Brittle materials like cast iron or glass fracture with little to no warning, while ductile materials typically show significant deformation first.
• Fatigue is progressive, localized damage from cyclic (repeated) loading. A classic example: bending a paperclip back and forth until it snaps. The applied stress can be well below the yield strength, yet the part still fails after enough cycles.
• Creep is the slow, permanent deformation of a material under constant stress, especially at elevated temperatures. Think of a plastic ruler sagging over time under a sustained load. Creep is a major concern in turbine blades and boiler components.
• Buckling is a sudden lateral deflection of a slender structural member under compressive load. A thin metal column, for instance, can collapse sideways long before the material itself reaches its compressive yield strength.

Surface Degradation

These modes don't involve bulk structural failure but gradually remove or weaken material at the surface.

• Wear is the removal of material from a surface through mechanical contact with another surface. Gear teeth abrading against each other over thousands of cycles is a common example.
• Corrosion is an electrochemical reaction between a material (usually a metal) and its environment. Steel rusting when exposed to moisture and oxygen is the most familiar case. Corrosion reduces cross-sectional area and can act as a stress concentrator, accelerating other failure modes.

Material Properties

Stress-Strain Behavior

The stress-strain curve is the foundational tool for understanding how a material responds to load. It plots stress (force per unit area, $\sigma$) on the vertical axis against strain (relative deformation, $\epsilon$) on the horizontal axis.

Two regions define the curve's shape:

• Elastic region: The material deforms under load but returns to its original shape when the load is removed. Stress and strain are proportional here, following Hooke's Law ($\sigma = E\epsilon$, where $E$ is the modulus of elasticity).
• Plastic region: Beyond the yield point, the material deforms permanently. Removing the load leaves a residual deformation.

Key points on the curve:

• Yield strength ($\sigma_y$) is the stress at which plastic deformation begins. For materials without a clear yield point (like many aluminum alloys), it's determined using the 0.2% offset method: draw a line parallel to the elastic portion of the curve, starting at 0.2% strain ($\epsilon = 0.002$). The stress where this line intersects the stress-strain curve is taken as $\sigma_y$.
• Ultimate tensile strength ($\sigma_u$) is the maximum stress the material can sustain. On the curve, it's the highest point. After this, necking begins in ductile materials and the engineering stress drops until fracture.

Strength Properties

Different loading conditions demand different strength measures. Each one describes resistance to a specific type of applied force:

• Tensile strength resists pulling forces that try to elongate or stretch the material apart. Example: a steel cable supporting a bridge deck.
• Compressive strength resists pushing forces that try to crush or shorten the material. Example: a concrete pillar carrying the weight of a building.
• Shear strength resists forces acting parallel to a cross-section, trying to slide one portion of the material past another. Example: a bolt in a lap joint holding two plates together. Shear strength is typically about 50–60% of tensile strength for most ductile metals.
• Torsional strength resists twisting moments applied about the longitudinal axis. Example: a drive shaft transmitting torque from an engine to the wheels. Torsion produces shear stress that varies from zero at the center to a maximum at the outer surface.

Understanding which strength property governs your design depends entirely on the loading scenario. A component under pure tension needs adequate tensile strength, but a bolted connection is often limited by shear. Identifying the dominant loading type is what connects material properties back to the failure modes above and, ultimately, to the failure theories covered in the rest of this unit.