Question 1

What is the relationship between stress intensity factor K_I and fracture toughness K_IC?

Accepted Answer

K_I characterizes the magnitude of the crack-tip stress field and is calculated as K_I = σ·√(π·a)·F(a/W), where F is the geometry correction factor. K_IC is the material's plane-strain fracture toughness, the critical value at which unstable fracture occurs. When K_I ≥ K_IC, brittle fracture is predicted. The safety factor is n = K_IC / K_I; a value of n ≥ 2 is the general design target. K_I / K_IC > 0.8 is a warning threshold for design review.

Question 2

When should J-integral be used instead of K_I?

Accepted Answer

In the linear elastic regime, J = K_I²/E' (where E' = E in plane stress and E/(1−ν²) in plane strain). J-integral becomes particularly valuable in elastic-plastic fracture mechanics (EPFM) when significant plasticity develops at the crack tip—for example, in low-strength, high-toughness steels or at stresses approaching the yield strength. The J_IC fracture toughness is measured per ASTM E1820 and is used to assess fracture in thick, constrained geometries where stress triaxiality is high. This tool calculates the elastic J-integral based on LEFM assumptions.

Question 3

What is the elliptic integral Φ used in the semi-elliptical surface crack K_I formula?

Accepted Answer

For a semi-elliptical surface crack, K_I = (σ/Φ)·√(π·a), where Φ is the complete elliptic integral of the second kind, depending on the aspect ratio a/c (crack depth to half-surface-length). The Raju-Newman approximation gives Φ ≈ √(1 + 1.464·(a/c)^1.65) for a/c ≤ 1. For a semicircular crack (a/c = 1), Φ ≈ 1.571, meaning K_I is lower than for a through-crack of the same half-length by this factor.

Question 4

How does plane stress versus plane strain affect fracture toughness?

Accepted Answer

Plane strain (thick section, high constraint) gives the minimum fracture toughness K_IC, the conservative value used in damage-tolerant design and measured per ASTM E399 / ISO 12135. Under plane stress (thin sheet, low constraint), the plastic zone at the crack tip is larger, and the apparent toughness K_c exceeds K_IC significantly. The plane strain thickness requirement is t ≥ 2.5·(K_IC/σ_y)². For thin components where plane stress dominates, K_c must be measured separately from R-curve testing.

J-Integral & Stress Intensity Factor (K_I) Calculator

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