Determination of stress intensity factor of sharp V-notch under pure shear loading by the caustic method

Liyun Yang; Huanning Hu; Ye Song; Yuh J. Chao; Yuh J. Chao

doi:10.1364/AO.408339

Applied Optics
Vol. 59,
Issue 32,
pp. 10168-10176
(2020)
•https://doi.org/10.1364/AO.408339

Determination of stress intensity factor of sharp V-notch under pure shear loading by the caustic method

Liyun Yang, Huanning Hu, Ye Song, and Yuh J. Chao

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Liyun Yang, Huanning Hu, Ye Song, and Yuh J. Chao, "Determination of stress intensity factor of sharp V-notch under pure shear loading by the caustic method," Appl. Opt. 59, 10168-10176 (2020)

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Abstract

The caustic method has proven to be a useful optical method to determine stress intensity factors. This paper evaluates the stress intensity factors of a sharp V-notch under pure shear loading by the caustic method for isotropic materials. The elastic stress fields and caustics formation near the V-notch tip under pure shear loading are first introduced. The theoretical relationship between the stress intensity factor of the sharp V-notch and the characteristic length is derived. Then, the experiment on the V-notched polymethyl methacrylate specimens under pure shear loading is carried out to obtain the stress intensity factor with the derived caustic formulation. Finally, the present results obtained from caustics are compared to the results available in the literature. The good accuracy of the results obtained demonstrates the ability of the caustics method in the determination of the stress intensity factor of a sharp V-notch.

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V-notch Angle	$ξ_{I I}$	V-notch Angle	$ξ_{I I}$
0°	0.5000	15°	0.5423
30°	0.5982	45°	0.6597
60°	0.7309	75°	0.8132
90°	0.9085	$\geq {102.5}^{\circ}$	1.0000

V-notch Angle	$α_{1}$	$α_{2}$
0°	74.61°	−93.72°
15°	75.93°	−93.85°
30°	77.69°	−93.95°
45°	79.62°	−93.94°
60°	81.86°	−93.76°
75°	84.42°	−93.23°
90°	87.32°	−92.06°
$\geq {102.5}^{\circ}$	90°	−90°

Specimen	$2 β (\deg .)$	$a (m m)$	$w (m m)$	$b (m m)$	$h (m m)$	$B (m m)$	$R (m m)$	$r (m m)$
Iosipescu specimen	30	60	100	33	37.5	10	-	-
Bank-Sills specimen1	0	20	30	6	36	6.4	190	40
Bank-Sills specimen2	0	30	30	6	36	6.4	190	40
Bank-Sills specimen3	30	10	30	6	36	6.4	190	40
Bank-Sills specimen4	30	20	30	6	36	6.4	190	40
Bank-Sills specimen5	60	10	30	6	36	6.4	190	40

Uniform Load p (MPa)	0.00	3.97	7.94	11.92	15.89	19.87	23.84	27.81
FEM $K_{V, I I}$	0.00	6.22	12.44	18.67	24.89	31.11	37.33	43.55
Caustic method $K_{V, I I}$	0.00	5.91	12.33	18.07	24.61	30.75	36.98	42.49
FEM $F_{V, I I}$	-	1.0339	1.0339	1.0335	1.0336	1.0332	1.0333	1.0334
Caustic method $F_{V, I I}$	-	0.9823	1.0247	1.0003	1.0220	1.0212	1.0236	1.0082
Relative error	-	−5.00%	−0.88%	−3.20%	−1.10%	−1.20%	−0.90%	−2.40%

				$F_{V, I I} = K_{V, I I} / τ_{0} \sqrt{π} a^{1 - ξ_{I I}}$
Specimen	$2 β$ (deg.)	a (mm)	P (N)	Present contribution	Banks-Sills and M Arcan [21]	FEM value	Relative Error
Bank-Sills specimen1	0	20	460	0.9831	1.0240	-	3.99%
Bank-Sills specimen2	0	30	400	1.0932	1.1460	-	4.61%
Bank-Sills specimen3	30	10	1600	1.2013	-	1.2350	2.73%
Bank-Sills specimen4	30	20	1600	1.3645	-	1.4154	3.60%
Bank-Sills specimen5	60	10	1600	1.6121	-	1.6392	1.65%

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Applied Optics