Compare Mode I stress intensity and plastic-zone estimates for CCT, SENT, CT and SENB specimens using explicit nominal-load definitions. Critical crack size is solved with a changing geometry factor, not a frozen correction.
Specimen Geometry
Loading & Crack
Applied stress σ (MPa)
MPa
Crack length a (mm)
mm
Specimen width W (mm)
mm
Material Properties
Fracture toughness K_Ic (MPa√m)
MPa√m
Yield stress σ_y (MPa)
MPa
Results
—
K_I (MPa√m)
—
Safety Factor K_Ic/K_I
—
Plastic zone r_p (mm)
—
Critical a_c (mm)
—
Geometry factor Y
Crack
Ka
Theory & Key Formulas
K_I = σ Y(a/W) √(πa); a [m]
rp [mm] = 1000 (K_I/σy)² / (2π) (plane stress)
K_I(ac) = K_Ic; solve with Y(ac/W), σ and W fixed
CT: σ = P/(BW); SENB: σ = 3PS/(2BW²), S=4W
Model and input definitions
This is a static, linear-elastic Mode I learning model. CCT uses crack length 2a and total plate width 2W; SENT uses crack length a and width W. For CT, enter σ=P/(BW). For SENB, enter nominal bending stress σ=3PS/(2BW²), with span S=4W. Equal σ values do not mean equal applied loads across specimen types.
Reproduce a result
Choose a specimen and enter σ in MPa, a and W in mm. CCT uses W as the half-width.
Set K_Ic and yield stress σy. Material presets are illustrative, not certified product properties.
Read the full-input result; on an animated view advance the load to its maximum or use reduced motion. Out-of-domain a/W values produce a warning instead of an extrapolated result.
Worked example
CCT with σ=100 MPa, a=10 mm, W=100 mm (total width 200 mm), K_Ic=50 MPa√m and σy=350 MPa gives x=0.1 and Y=1/√cos(πx/2)=1.0062. K_I=17.83 MPa√m, plane-stress rp=0.413 mm and K_Ic/K_I=2.80. Doubling σ doubles K_I and quadruples rp.
🙋
What should I check in this example?
🎓
Change one input at a time and compare the formula with the displayed result. Read the full-input result; on an animated view advance the load to its maximum or use reduced motion. Out-of-domain a/W values produce a warning instead of an extrapolated result.
Limits and interpretation
CCT uses the Feddersen long-plate approximation. This tool restricts SENT to 0<a/W≤0.6, CT to 0.2≤a/W≤0.8 and CCT/SENB to 0<a/W≤0.8. A critical size outside the domain is shown as a < or > bound, not extrapolated. The first-order plastic zone assumes plane stress. Thickness, remaining ligament and small-scale yielding need separate checks. Fatigue life and inspection intervals are not calculated.
Frequently asked questions
No. With σ and W fixed, the solver updates Y(a/W) and uses bisection to solve K_I(a)=K_Ic.
Yes: mm. With K in MPa√m and σy in MPa, the formula produces metres, which are multiplied by 1000.
For CT the input is the equivalent nominal value σ=P/(BW), not a remote tensile stress.
The tool reports an unsupported geometry rather than silently replacing the crack length with 0.99W. Choose valid specimen dimensions.
Checks cover displayed units, reference calculations, input sensitivity, boundary conditions and cross-language results. They do not certify code compliance or real-world accuracy.