Local stress analysis of blunt V-notches using the digital gradient sensing method

Wei Liu; Longkang Li; Yaxu Qiao

doi:10.1364/AO.416708

Applied Optics
Vol. 60,
Issue 6,
pp. 1489-1499
(2021)
•https://doi.org/10.1364/AO.416708

Local stress analysis of blunt V-notches using the digital gradient sensing method

Wei Liu, Longkang Li, and Yaxu Qiao

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Wei Liu, Longkang Li, and Yaxu Qiao, "Local stress analysis of blunt V-notches using the digital gradient sensing method," Appl. Opt. 60, 1489-1499 (2021)

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Abstract

In this study, the digital gradient sensing (DGS) method is extended to determine the local stress fields at the blunt V-notch tip. Completely analytical expressions for angular deflections of light beams in the vicinity of the blunt V-notch tip are deduced based on Filippi’s stress equation. Under plane stress conditions, the patterns of angular deflection related to two orthogonal stress gradients are theoretically plotted, and the effects of notch angle and notch radius are synthetically investigated, respectively. New procedures for the evaluation of local stress components and generalized notch stress intensity factor (NSIF) are presented using the experimental patterns of angular deflection contours. The NSIF values at the blunt V-notch tip in polymer materials with different geometric parameters under three-point-bend loading conditions are extracted from the DGS measurements. A good agreement is observed between the experimental data and the finite element simulations, which can verify the effectiveness and accuracy of the proposed DGS method.

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$2 α$	$q$	$λ_{1}$	$μ_{1}$	$χ_{b_{1}}$	$χ_{c_{1}}$	$χ_{d_{1}}$
0	2.000	0.5	−0.5	1	4	0
$π / 6$	1.8333	0.5014	−0.4561	1.0707	3.7907	0.0632
$π / 4$	1.7500	0.5050	−0.4319	1.1656	3.5721	0.0828
$π / 3$	1.6667	0.5122	−0.4057	1.3123	3.2832	0.0960
$π / 2$	1.5000	0.5448	−0.3449	1.8414	2.5057	0.1046
$2 π / 3$	1.3334	0.6157	−0.2678	3.0027	1.5150	0.0871

No.	$2 α$	$ρ$ (mm)	$a$ (mm)	$W$ (mm)	$L$ (mm)	$H$ (mm)	$t$ (mm)
S1	0	0.5	10	140	160	40	5
S2	$π / 6$	0.5	10	140	160	40	5
S3	$π / 4$	0.5	10	140	160	40	5
S4	$π / 3$	0.5	10	140	160	40	5
S5	$π / 2$	0.5	10	140	160	40	5
S6	$3 π / 2$	0.5	10	140	160	40	5
S7	$π / 3$	1.5	10	140	160	40	5
S8	$π / 3$	2.5	10	140	160	40	5
S9	$π / 3$	0.5	15	140	160	40	5
S10	$π / 3$	0.5	20	140	160	40	5

$N_{O}$ .	$2 α$	$ρ$ (mm)	$a$ (mm)	$k_{s}$ ( $M P a \cdot m^{1 - λ_{1}} / N$ )	Fracture load ${\bar{P}}_{C}$ (N)	$K_{C}^{V, ρ}$ ( $M P a \cdot m^{1 - λ_{1}}$ )
S1	0	0.5	10	0.00678	454	3.08
S2	$π / 6$	0.5	10	0.00702	462.3	3.24
S3	$π / 4$	0.5	10	0.00732	475	3.47
S4	$π / 3$	0.5	10	0.00781	483.3	3.77
S5	$π / 2$	0.5	10	0.00869	544	4.73
S6	$3 π / 2$	0.5	10	0.0118	648.7	7.65
S7	$π / 3$	1.5	10	0.00715	766	5.47
S8	$π / 3$	2.5	10	0.00584	1209	7.06
S9	$π / 3$	0.5	15	0.00853	397	3.39
S10	$π / 3$	0.5	20	0.00980	337	3.30

$2 α$	$q$	$λ_{1}$	$μ_{1}$	$χ_{b_{1}}$	$χ_{c_{1}}$	$χ_{d_{1}}$
0	2.000	0.5	−0.5	1	4	0
$π / 6$	1.8333	0.5014	−0.4561	1.0707	3.7907	0.0632
$π / 4$	1.7500	0.5050	−0.4319	1.1656	3.5721	0.0828
$π / 3$	1.6667	0.5122	−0.4057	1.3123	3.2832	0.0960
$π / 2$	1.5000	0.5448	−0.3449	1.8414	2.5057	0.1046
$2 π / 3$	1.3334	0.6157	−0.2678	3.0027	1.5150	0.0871

No.	$2 α$	$ρ$ (mm)	$a$ (mm)	$W$ (mm)	$L$ (mm)	$H$ (mm)	$t$ (mm)
S1	0	0.5	10	140	160	40	5
S2	$π / 6$	0.5	10	140	160	40	5
S3	$π / 4$	0.5	10	140	160	40	5
S4	$π / 3$	0.5	10	140	160	40	5
S5	$π / 2$	0.5	10	140	160	40	5
S6	$3 π / 2$	0.5	10	140	160	40	5
S7	$π / 3$	1.5	10	140	160	40	5
S8	$π / 3$	2.5	10	140	160	40	5
S9	$π / 3$	0.5	15	140	160	40	5
S10	$π / 3$	0.5	20	140	160	40	5

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Applied Optics