Stress Intensity Factor Simulator — Linear Elastic Fracture Mechanics
Mode I K_I = Y sigma sqrt(pi a) computed in real time. Evaluate safety factor, critical crack length and fracture stress with sliders. Crack diagram and K_I vs a chart visualize how close you are to fracture.
Geometry & Material Presets
Live fracture simulation — crack-tip stress singularity (1/√r)
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Stress intensity K_I [MPa√m]
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Crack length a [mm]
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Shape factor Y
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Applied stress σ [MPa]
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Status
Results
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Stress intensity factor K_I
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Safety factor SF
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Critical crack length a_crit
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Fracture stress sigma_crit
Crack geometry diagram (stress concentration)
K_I vs crack length a — intersection with K_IC gives a_crit
Theory & Key Formulas
$$K_I = Y\,\sigma\,\sqrt{\pi a}$$
Y is the shape factor (1.0 for a center through-crack, 1.12 for an edge crack), sigma is the remote nominal stress in MPa, and a is the crack length in metres.
Unstable fracture occurs when K_I reaches K_IC. SF<1 means immediate fracture, a_crit is the crack length that triggers fracture under the current stress, and sigma_crit is the stress that triggers fracture at the current crack length.
What is the Stress Intensity Factor Simulator?
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What exactly is the stress intensity factor? How is K_I different from regular stress sigma? I keep hearing that a crack changes everything.
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Great question. At the tip of a sharp crack, linear elastic theory predicts an infinite stress. So sigma alone is useless there. Instead we measure the strength of that singular field with K_I = Y sigma sqrt(pi a). a is the crack length, Y is the geometry factor. Try sliding a from 5 mm to 10 mm in the tool: K_I jumps from about 28 to 40 MPa·√m.
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So if K_I exceeds the fracture toughness K_IC the part breaks? And SF below 1 means I am already in trouble?
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Exactly. K_I greater than or equal to K_IC means unstable fracture, the part snaps. SF = K_IC/K_I is the safety factor. Real designs aim for SF of 2 to 3 because nobody wants to live near 1. Slide sigma from 200 to 300 MPa and watch SF drop from 1.78 to 1.19. Same crack, very different risk.
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What is the critical crack length a_crit then? Is it the largest crack I can tolerate in service?
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Yes. a_crit = (K_IC/(Y sigma))^2 / pi is the crack length that triggers fracture at the current stress. At sigma = 200 MPa and Y = 1.12 the tool shows about 15.9 mm. In practice you set the inspection limit to a_crit/2 or smaller and choose the inspection interval so a crack found today cannot reach that limit before the next check. The red dashed line in the chart is K_IC and the intersection with the blue K_I curve is exactly a_crit.
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Why is the shape factor Y about 1.12 for an edge crack but only 1.0 for a center crack?
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An edge crack has a free surface on one side, so the stress field cannot escape symmetrically. The crack tip sees a stronger singularity. The classical free-surface correction for an edge crack in a semi-infinite plate is 1.1215. Welded toes, sharp corners and machined notches behave essentially as edge cracks, so using Y = 1.12 is the realistic conservative choice for those geometries.
FAQ
In theory SF greater than or equal to 1 prevents fracture, but real components face load variation, temperature shifts, corrosion, scatter in material data and uncertainty in NDE crack sizing. Standard practice requires SF of 2 to 3. Pressure vessel codes such as ASME BPVC and JIS B 8265 commonly use SF = 3.
K_IC is measured by ASTM E399 or JIS Z 2284 using compact tension (CT) or three-point bend specimens under plane-strain conditions. Thin specimens develop large plastic zones and produce higher apparent K_C values. The converged value at sufficient thickness is K_IC (plane-strain fracture toughness). Designs of thin sheet should use more conservative data.
No. This tool assumes linear elastic fracture mechanics (LEFM), where the crack-tip plastic zone is small compared with a. If the plastic zone exceeds a/50 you should apply the Irwin correction (effective crack length a + r_y) or, more rigorously, switch to elastic-plastic fracture mechanics (J-integral, CTOD).
Use SIF handbooks (Tada, Paris and Irwin) or databases such as BS 7910 and NASGRO, which tabulate Y(a/W) for many specimen geometries and crack locations. When no data is available, a conservative Y of about 1.5 is sometimes used, or K_I is computed directly with finite element analysis.
Real-world applications
Pressure vessels and piping: Defects found during periodic inspection (weld flaws, SCC, corrosion pits) are evaluated by computing K_I at operating pressure and comparing with K_IC. LEFM underpins the in-service flaw assessment of ASME BPVC Section XI.
Aircraft damage-tolerant design: Starting from an assumed initial flaw, K_I is checked against K_IC and combined with the Paris law to estimate the cycles to reach a_crit. Inspection intervals are typically set to half of that life.
Nuclear pressurized thermal shock (PTS): Reactor pressure vessels suffer K_IC reduction from neutron embrittlement. PTS analyses verify that K_I during a postulated cold-water injection event remains below the shifted K_IC at the lowest service temperature.
Bridges and storage tanks: Fatigue cracks detected at welded joints are assessed by comparing K_I with K_IC. Locations with SF below 2 are prioritized for repair, drilling stop holes or applying bolted patches.
Common misconceptions and pitfalls
The most frequent confusion is that sigma in K_I = Y sigma sqrt(pi a) is the remote nominal stress, not the local crack-tip stress. Do not multiply by a stress concentration factor K_t. Stress concentration applies to blunt notches; stress intensity applies to sharp cracks. They are different concepts and double-counting will badly overestimate K_I.
Second, the shape factor Y is rarely constant. This tool lets you set Y with a slider, but in real structures Y depends on a/W (crack length over part width). As the crack grows, Y also grows, so K_I rises faster than the simple sqrt(a) law suggests. Always check finite-width corrections.
Third, K_IC is not a single material constant. It depends on temperature, plate thickness, strain rate and environment (hydrogen, seawater). Below the ductile-to-brittle transition temperature K_IC can drop dramatically; the Liberty ships and the Hoan Bridge in Milwaukee are historical reminders. Use K_IC data measured for the actual service condition.
Set applied stress (slSigma) in MPa using the slider; typical range 50–500 MPa for steel structures
Adjust crack length (slA) in mm; common inspection detection limits range 0.5–5 mm
Define geometry factor (slY) from 1.0 to 2.0; use Y=1.12 for edge cracks, Y=1.77 for corner cracks
Enter material fracture toughness K_IC (slKIC) in MPa√m; 6500–7000 MPa√m for 4340 steel, 2500–3000 for 7075-T6 aluminum
Read K_I, safety factor SF = K_IC/K_I, critical crack length a_crit, and fracture stress σ_crit in real time
Worked Example
A 4340 steel pressure vessel operates at σ = 250 MPa with detected surface crack a = 2.0 mm and stress concentration Y = 1.12. With K_IC = 6800 MPa√m: K_I = 1.12 × 250 × √(π × 0.002) = 14.1 MPa√m, yielding SF = 6800/14.1 = 482. Critical crack length a_crit = (6800/(1.12 × 250))² / π = 33.2 mm. If stress increases to 380 MPa, K_I rises to 21.4 MPa√m and SF drops to 318, demonstrating how modest load increases accelerate crack propagation risk.
Practical Notes
Use Y = 1.0 for internal penny cracks, Y = 1.12 for semi-elliptical surface defects, and Y = 1.77 for corner cracks; finite element correction factors improve accuracy for a/t > 0.3
Welded joints in 316L stainless steel typically show K_IC ≈ 7200 MPa√m but reduced toughness (≈5500) in heat-affected zones; verify post-weld heat treatment impact
Critical crack length becomes physically impossible when K_I exceeds K_IC; SF < 1.0 signals imminent failure—schedule immediate inspection or reduce operating stress
Fatigue crack growth follows Paris law (da/dN = C(ΔK_I)^m); use this simulator to identify stress thresholds preventing sub-critical propagation in cyclic loading