Technical Reference¶
Crack Growth Equations¶
XdTd supports two fatigue crack growth equations. The equation and its parameters are defined in the material properties of the sheet.
Paris Law¶
| Parameter | Description |
|---|---|
| \(C\) | Material constant |
| \(m\) | Exponent |
| \(\Delta K\) | Stress intensity factor range (\(K_{max} - K_{min}\)) |
The Paris law is the simplest model — it describes the linear region (Region II) of the da/dN vs. \(\Delta K\) curve on a log-log plot.
Forman Equation¶
| Parameter | Description |
|---|---|
| \(C\) | Material constant |
| \(m\) | Exponent |
| \(R\) | Stress ratio (\(\sigma_{min} / \sigma_{max}\)) |
| \(K_c\) | Fracture toughness |
The Forman equation accounts for the stress ratio effect and the acceleration of crack growth as \(K\) approaches the fracture toughness \(K_c\).
Stress Intensity Factor Methods¶
XdTd computes Mode I and Mode II stress intensity factors using two methods:
| Method | Accuracy | Description |
|---|---|---|
| J-Integral (JINT) | ~1% | Path-independent energy integral evaluated around the crack tip. Default and recommended. |
| Crack Opening Displacement (CROD/COD) | ~5% | Based on the relative displacement of the crack faces near the tip. |
The method is selected in the Analysis Parameters dialog before running an analysis.
Crack Growth Direction¶
The maximum tangential stress criterion is used to determine the crack growth direction under mixed-mode loading. The crack turns to eliminate Mode II, growing in pure Mode I. This is confirmed by \(K_{II}\) remaining approximately zero along the computed growth path.
Fastener Flexibility Formulas¶
For fastened (riveted/bolted) attachments, XdTd computes the joint flexibility using one of four industry-standard formulas:
| Formula | Description |
|---|---|
| Douglas | Default. Based on Douglas Aircraft Company empirical data. |
| Huth | Semi-empirical formula widely used in aerospace. |
| Grumman | Based on Grumman Aerospace Corporation test data. |
| Direct | User-specified flexibility value (no formula). |
The formula is selected in the Analysis Parameters dialog.
Analysis Parameters¶
| Parameter | Description | Default |
|---|---|---|
| 2D Case | Plane Stress or Plane Strain | Plane Stress |
| Attachment Behaviour | Elastic or Elastic-Plastic for stiffener/patch attachments | Elastic |
| SIF Method | JINT (J-Integral) or CROD (Crack Opening Displacement) | JINT |
| Crack Growth | Enable/disable crack propagation analysis | Disabled |
| Number of Increments | Crack growth steps | 1 |
| Stress Ratio (R) | \(\sigma_{min} / \sigma_{max}\) for fatigue loading | 0.0 |
| Straight Growth | Force crack to grow straight (no direction change) | Yes |
| Mesh Refinement | Slider controlling element density (0–4) | Level 2 |
| Internal Points | Compute stresses at internal field points for contour plots | Enabled |
| Fastener Formula | Flexibility formula for fastened joints | Douglas |
| Convergence Profile | Crack growth convergence tolerance level (1–5) | 3 |
File Format¶
Case studies are saved as .xdtd files, which are SQLite databases. Each file is self-contained — geometry, material properties, mesh parameters, boundary conditions, and results are all stored in a single file.
Files can be inspected with any SQLite browser (e.g., DB Browser for SQLite) if needed.
Material Database¶
XdTd ships with built-in databases for materials, fasteners, and adhesive bonds. These are provided for completeness only — the use of the properties therein is the sole responsibility of the user. XdTd provides tools for users to create and manage their own databases.
Units
XdTd is unit-agnostic — it does not enforce any unit system. The units are entirely defined by the values in your database. All properties must use a consistent unit system. The distributed database uses MPa and mm throughout.
Material Properties¶
| Property | Description |
|---|---|
| Elasticity Modulus (\(E\)) | Young's modulus |
| Poisson's Ratio (\(\nu\)) | |
| Thickness (\(t\)) | Sheet thickness |
| Yield Strength (\(\sigma_y\)) | |
| Fracture Toughness (\(K_c\)) | Critical SIF |
| CG Equation | Paris or Forman |
| CG Constant (\(C\)) | Crack growth law constant |
| CG Exponent (\(m\)) | Crack growth law exponent |
Fastener Properties¶
| Property | Description |
|---|---|
| Diameter | Fastener diameter |
| Modulus | Fastener material modulus |
| Strength | Fastener shear strength |
| Pitch | Spacing between fasteners |
Adhesive Bond Properties¶
| Property | Description |
|---|---|
| Thickness | Adhesive layer thickness |
| Shear Modulus (\(G_a\)) | Adhesive shear modulus |
| Shear Strength (\(\tau_a\)) | Adhesive shear strength |
| Yield Strain | |
| Ultimate Strain |