What is stress concentration factor Kt?

Kt is the ratio of maximum local stress to nominal stress at a geometric discontinuity. Kt = σ_max / σ_nom. It depends only on geometry, not material. A circular hole in a wide plate under tension has Kt ≈ 3.0.

What causes stress concentrations?

Any abrupt change in geometry: holes, notches, fillets, keyways, threads, grooves, changes in cross-section. The stress flow lines crowd together at these features, increasing local stress.

How does Kt affect fatigue life?

Stress concentrations dramatically reduce fatigue life because fatigue cracks initiate at the point of highest stress. The fatigue notch factor Kf ≤ Kt accounts for material sensitivity: Kf = 1 + q(Kt-1), where q is the notch sensitivity factor.

How can stress concentrations be reduced?

Use generous fillet radii, avoid sharp corners, use gradual transitions, add relief grooves near shoulders, polish surfaces at critical points, and use shot peening to introduce beneficial compressive residual stress.

What is Peterson's Stress Concentration Factors?

Peterson's is the definitive reference book containing charts and equations for Kt values for hundreds of geometric configurations. It provides Kt as a function of geometric ratios (r/d, D/d, etc.) for tension, bending, and torsion loading.

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使用簡化的 Peterson’s 圖表資料，查詢常見幾何形狀的 Kt 值——板中孔、軸肩圓角、U 型缺口。

Peterson’s 圖表Kt 查詢#173

結果

應力集中係數 Kt

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最大局部應力 σ_max

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幾何比例

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應力集中係數

典型 Kt 值

幾何形狀	Kt 範圍
寬板中央孔	~3.0（小 d/W）
軸肩圓角（D/d=2，r/d=0.1）	~1.8–2.5
U 型缺口	~1.5–3.5
環向溝槽	~1.5–3.0

⚠️ 注意： 這些是來自簡化曲線擬合方程式的近似值。如需精確值，請查閱 Peterson’s Stress Concentration Factors 或執行 FEA。Kt 僅適用於彈性分析。

應力集中係數 Kt 計算器 | Vibromera

結果

應力集中係數

典型 Kt 值

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