Design equation for stress concentration factors of notched strips and grooved shafts

Kato, Akira

doi:10.1243/03093247v271021

Cited by 17 publications

(23 citation statements)

References 22 publications

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“…The bar with the single semicircular groove in Figure 4 was used as a benchmark for the thermal analogy method. The stress results from the analogy were compared with the theoretical solution available in the literature [15][16][17] and with the outcome of a conventional 3D FE analysis. This step of the analysis allowed the accuracy and the efficiency of the thermal method to be assessed against established results and procedures.…”

Section: Geometriesmentioning

confidence: 99%

“…An accurate comparison among data from different sources is drawn in a paper by Hasegawa and Kuriyama,19 including also data from Matthews and Hooke. 20 The theoretical stress concentration factor for the same geometry is K t = 1.4892 and the procedure in Appendix 2 15 gives the value K t = 1.491. Although comparable in terms of accuracy, with respect to the 3D FE model, the 2D thermal analogy model proved much easier to implement and quicker to execute.…”

Section: Stress Concentration Factormentioning

confidence: 99%

“…For each combination of dimensionless variables (r/t, t/P and d/r), the prediction of the stress concentration obtained using Neuber's method is also provided (hollow circles). Neuber's predictions were obtained from Kato's equation 15 for the twisted bar with single Ugroove summarized in Appendix 2. At any occurrence, the depth t in Kato's equation was replaced with the reduced depth t * = g t, with g given by (1).…”

Section: Stress Concentration Factormentioning

confidence: 99%

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Concentration of torsional shear stresses in axisymmetric bars with deep periodic grooves

Castagnetti

Dragoni

2012

The Journal of Strain Analysis for Engineering Design

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The torsional stresses in round bars with deep periodic grooves are calculated by means of the formal analogy between the elastic problem and an auxiliary thermal problem. The analogy allows demanding three-dimensional analyses to be replaced with light two-dimensional analyses, easily implemented on general-purpose finite element packages. Following Neuber’s equivalence concept, the stress concentration in each periodically grooved bar is independently calculated by referring to a single groove of like geometry but lesser depth. Neuber’s approach predicts very closely the reference numerical results if supplemented with a heuristic depth correction function formerly developed by the authors for shallow periodic notches under torsion

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Section: Geometriesmentioning

confidence: 99%

Section: Stress Concentration Factormentioning

confidence: 99%

Section: Stress Concentration Factormentioning

confidence: 99%

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Concentration of torsional shear stresses in axisymmetric bars with deep periodic grooves

Castagnetti

Dragoni

2012

The Journal of Strain Analysis for Engineering Design

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“…In the elastic deformation, Fig. 12 shows that the longitudinal stress has a concave distribution on the net section, and r x at the notch root is equal to the maximum longitudinal stress (Leven and Frocht, 1952;Nishida, 1974;Kato, 1991;Noda et al, 1995;Pilkey, 1997). The concave distribution of r x becomes mild or mildly convex as the plastic deformation develops from the notch root.…”

Section: The Significance Of the New Sncfmentioning

confidence: 99%

“…Many analytical, numerical and experimental studies have been done on the elastic stress-concentration factor (SSCF) for various types of notch under tension and under bending (Leven and Frocht, 1952;Nishida, 1974;Kato, 1991;Noda et al, 1995;Pilkey, 1997). NeuberÕs analytical results have been the main source for the effect of notch depth on the elastic SSCF Pilkey (1997).…”

Section: Introductionmentioning

confidence: 99%

Effect of notch depth on strain-concentration factor of rectangular bars with a single-edge notch under pure bending

Tlilan

Sakai

Majima

2006

International Journal of Solids and Structures

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The FEM is employed to study the effect of notch depth on a new strain-concentration factor (SNCF) for rectangular bars with a single-edge notch under pure bending. The new SNCF K new e is defined under the triaxial stress state at the net section. The elastic SNCF increases as the net-to-gross thickness ratio h 0 /H 0 increases and reaches a maximum at h 0 /H 0 = 0.8. Beyond this value of h 0 /H 0 it rapidly decreases to the unity with h 0 /H 0 . Three notch depths were selected to discuss the effect of notch depth on the elastic-plastic SNCF; they are the extremely deep notch (h 0 /H 0 = 0.20), the deep notch (h 0 /H 0 = 0.60) and the shallow notch (h 0 /H 0 = 0.95). The new SNCF increases from its elastic value to the maximum as plastic deformation develops from the notch root. The maximum K new e of the shallow notch is considerably greater than that of the deep notch. The elastic K new e of the shallow notch is however less than that of the deep notch. Plastic deformation therefore has a strong effect on the increase in K new e of the shallow notch. The variation in K new e with M/M Y , the ratio of bending moment to that at yielding at the notch root, is slightly dependent up to the maximum K new e for the shallow notch. This dependence is remarkable beyond the maximum K new e . On the other hand, the variation in K new e with M/M Y is independent of the stress-strain curve for the deep and extremely deep notches.

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Stress concentrations in periodic notches: a critical investigation of Neuber's method

Castagnetti¹,

Dragoni

2013

Materialwissenschaft Werkst

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The work investigates the stress concentrations produced by periodic notches (i. e. uniformly repeated) in elastic solids under different loading conditions. Neuber's criterion, which likens the effect of a periodic notch to a single notch of similar profile but lesser depth, is critically examined. The criterion simply correlates the depth reduction factor to the ratio between the depth and the pitch of the original periodic notch, regardless of its shape. By examining literature results in periodic notches on circular bars and plane strips under torsion or axial loads, the work proves the accuracy of the Neuber's method for the ideal configuration of a sharp and shallow notch under shear stresses. By contrast, for real notches with a large root radius and finite depth, the accuracy is very poor, in particular for normal stresses. However, it is found that by simply ‘repairing’ the expression of the depth reduction factor and distinguishing between notches under shear or normal stresses, the criterion provides very accurate results, and becomes quite useful for real geometries

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Design equation for stress concentration factors of notched strips and grooved shafts

Cited by 17 publications

References 22 publications

Concentration of torsional shear stresses in axisymmetric bars with deep periodic grooves

Concentration of torsional shear stresses in axisymmetric bars with deep periodic grooves

Effect of notch depth on strain-concentration factor of rectangular bars with a single-edge notch under pure bending

Stress concentrations in periodic notches: a critical investigation of Neuber's method

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