Use of holographic optical elements in speckle metrology. Part 3: application to fracture mechanics

Chandra Shakher; Hira Lal Yadav

doi:10.1364/AO.30.003607

Applied Optics
Vol. 30,
Issue 25,
pp. 3607-3611
(1991)
•https://doi.org/10.1364/AO.30.003607

Use of holographic optical elements in speckle metrology. Part 3: application to fracture mechanics

Chandra Shakher and Hira Lal Yadav

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Chandra Shakher and Hira Lal Yadav, "Use of holographic optical elements in speckle metrology. Part 3: application to fracture mechanics," Appl. Opt. 30, 3607-3611 (1991)

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Abstract

In this work a two-hololens imaging system has been used to measure crack-mouth opening displacement and crack-tip opening displacement to determine the stress intensity factor K_I, the crack-tip plastic zone size r_p*, and the rotational factor r in a beam specimen having the central edge crack subjected to three-point bending using focused plane speckle photography. Experimental results are in good agreement with theoretical predictions. Current experimental investigations establish that low-cost holographic optics can be advantageously used in speckle metrology to solve complex problems of fracture mechanics.

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Load (P) (kg)	Distance Between Screen and Specklegram (D) (mm)	Fringe Spacing (β) (mm)	Magnitude of Displacement \|d\| = λD/β (μm)	Fringe Orientation (θ) with Respect to the X axis (deg)	CMOD		Percentage Deviation of CMOD (%)

					Expt =2\|d\|sinθ (μm)	Theor (μm)
5	350	16.30	13.59	4.00	1.90	2.08	8.7
7	350	10.90	20.32	3.75	2.66	2.90	8.3
9	350	7.90	28.04	3.50	3.42	3.74	8.6
11	350	6.00	36.91	3.25	4.19	4.57	8.3

Load (P) (kg)	Experimental Values of COD at a Point 4 mm Above Crack Mouth Opening: (COD)_y _=4mm					CMOD Expt (μm)	CTOD		Percentage Deviation of CTOD's (%)

	Distance Between Screen and Specklegram (D) (mm)	Fringe Spacing (β) (mm)	Magnitude of Displacement \|d\| = λD/β (μm)	Fringe Orientation (θ) with Respect to the X-axis (deg)	(COD)_y=4mm (μm)

							Expt (μm)	Theor (μm)
5	350	16.60	13.34	2.1	0.978	1.90	0.056	0.065	13.8
7	350	11.15	19.86	2.0	1.386	2.66	0.112	0.128	12.5
9	350	8.58	25.81	2.0	1.802	3.42	0.184	0.212	13.2
11	350	6.92	32.01	2.0	2.234	4.19	0.278	0.320	13.1

Load (P) (kg)	Experimental/Theoretical Values of K_I			Experimental/Theoretical Values of r_p*			Experimental/Theoretical Values of r

	(K_I)		Percentage Deviation of K_I (%)	r_p*		Percentage Deviation of r_p* (%)	r		Percentage Deviation of r (%)

	Expt [kg (mm)^−3/2]	Theor [kg (mm)^−3/2]		Expt (μm)	Theor (μm)		Expt (μm)	Theor (μm)
5	2.35	2.53	7.1	2.90	3.39	14.5	0.0203	0.0215	5.6
7	2.32	3.54	6.2	5.81	6.63	14.1	0.0293	0.0308	4.9
9	4.25	4.56	6.8	9.54	10.99	13.2	0.0379	0.0401	5.5
11	5.23	5.57	6.1	14.42	16.40	12.1	0.0474	0.0502	5.6

Load (P) (kg)	Distance Between Screen and Specklegram (D) (mm)	Fringe Spacing (β) (mm)	Magnitude of Displacement \|d\| = λD/β (μm)	Fringe Orientation (θ) with Respect to the X axis (deg)	CMOD		Percentage Deviation of CMOD (%)

					Expt =2\|d\|sinθ (μm)	Theor (μm)
5	350	16.30	13.59	4.00	1.90	2.08	8.7
7	350	10.90	20.32	3.75	2.66	2.90	8.3
9	350	7.90	28.04	3.50	3.42	3.74	8.6
11	350	6.00	36.91	3.25	4.19	4.57	8.3

Load (P) (kg)	Experimental Values of COD at a Point 4 mm Above Crack Mouth Opening: (COD)_y _=4mm					CMOD Expt (μm)	CTOD		Percentage Deviation of CTOD's (%)

	Distance Between Screen and Specklegram (D) (mm)	Fringe Spacing (β) (mm)	Magnitude of Displacement \|d\| = λD/β (μm)	Fringe Orientation (θ) with Respect to the X-axis (deg)	(COD)_y=4mm (μm)

							Expt (μm)	Theor (μm)
5	350	16.60	13.34	2.1	0.978	1.90	0.056	0.065	13.8
7	350	11.15	19.86	2.0	1.386	2.66	0.112	0.128	12.5
9	350	8.58	25.81	2.0	1.802	3.42	0.184	0.212	13.2
11	350	6.92	32.01	2.0	2.234	4.19	0.278	0.320	13.1

Abstract

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Tables (3)

Equations (13)

Applied Optics