Fracture Mechanics — CAE Glossary

Good question. Ordinary strength calculation assumes the material is sound — meaning cracks don't exist — and checks whether stress remains below an allowable value. But real structures always contain some form of discontinuity: welding defects, fatigue cracks, corrosion pits. That's where fracture mechanics comes in.

Exactly. Fracture Mechanics is the science of quantitatively assessing whether an existing crack will remain stable or lead to unstable fracture (sudden rupture). For example, if engineers discover a small crack in an aircraft fuselage, fracture mechanics lets them predict whether the crack will grow to a critical size before the next inspection. This underpins damage-tolerant design.

Completely different. The stress concentration factor $K_t$ is a dimensionless ratio showing how many times the nominal stress amplifies near a notch or hole. The stress intensity factor $K$, on the other hand, has units of $\mathrm{MPa}\sqrt{\mathrm{m}}$ and quantifies the strength of the stress field at the crack tip itself. Its definition is:

It refers to the crack deformation mode. Perfect timing to discuss the different crack modes.

Yes, three of them. These are critically important in practice, so learn them well.

Basically yes. That's the failure criterion for LEFM (Linear Elastic Fracture Mechanics). But there's an important precondition. Let me explain the difference between LEFM and EPFM.

LEFM is Linear Elastic Fracture Mechanics, and EPFM is Elastic-Plastic Fracture Mechanics. Roughly speaking, you pick based on whether the plastic zone at the crack tip is small or large.

LEFM is valid under Small-Scale Yielding (SSY) conditions, when the plastic zone size $r_p$ is much smaller than the crack length $a$ or specimen dimensions. Irwin's plastic zone estimate gives:

Roughly, but it's not that simple. Even a ductile material can exhibit brittle fracture at low temperature or in thin sections (plane strain). Conversely, a high-strength steel in thick plates can show plasticity. Industry codes like ASME BPVC Section XI and BS 7910 use the FAD (Failure Assessment Diagram) to handle both LEFM and EPFM in a unified framework.

Intuitively, it's the energy released when a crack extends by a unit area. Defined by Rice (1968) as a path integral around the crack tip:

That's the magic — J is path-independent. You get the same value whether you compute it very close to the crack tip or far from it. This is huge for FEM: even if your crack-tip mesh isn't perfectly refined, you can compute J accurately on outer contours. Abaqus and other solvers automatically compute J over multiple contours so you can verify convergence.

Under small-scale yielding, there's a direct relationship:

In traditional FEM, you must align mesh element boundaries along the crack surface. The crack tip has a $1/\sqrt{r}$ stress singularity, so you place quarter-point singular elements (with mid-side nodes at 1/4 position) there. Every time the crack grows, you remesh. In 3D, this becomes incredibly tedious.

Exactly. XFEM augments standard FEM shape functions with enrichment functions:

Abaqus 6.9 and later have XFEM as a standard feature, making crack insertion and growth relatively straightforward. ANSYS Mechanical offers Smart Crack Growth. Open-source Code_Aster supports X-FEM too. But XFEM isn't a panacea — complex 3D crack branching and contact-aided fracture still pose challenges. For those cases, Cohesive Zone Model (CZM) or phase-field methods are worth considering.

The mesh at the crack tip. For traditional FEM, create a concentric "spiderweb" mesh with singular quarter-point elements and collapse the crack-tip nodes to a single point. The innermost element size should be 1/20 of the crack length or smaller. Use 5–10 contours for J-integral computation and verify convergence on the outer contours.

First, compute the stress intensity factor range $\Delta K = K_{\max} - K_{\min}$ at each load cycle. Then apply the Paris law to get the crack growth rate:

Here's a quick guide: