Strength analysis of composite cables

Luz, Felipe Ferreira; Menezes, Eduardo Antonio Wink de; Silva, Laís Vasconcelos da; Cimini Jr., Carlos Alberto; Amico, Sandro Campos

doi:10.1590/1679-78254177

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Latin American Journal of Solids and Structures

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Original Article • Lat. Am. j. solids struct 15 (4) • 2018 • https://doi.org/10.1590/1679-78254177 copy

Strength analysis of composite cables

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Carbon Fiber Reinforced Polymer (CFRP) cables, due to their outstanding performance in terms of specific stiffness and strength, are usually found in civil construction applications and, more recently, in the Oil & Gas sector. However, experimental data and theoretical solutions for these cables are very limited. On the contrary, several theoretical and numerical approaches are available for isotropic cables (metallic wire ropes), some of them with severe simplifications, nonetheless showing good agreement with experimental data. In this study, experimental tensile results for 1×7 CRFP cables were compared to a simplified analytical model (assumed transversally isotropic) and to a 3D finite element model incorporating the experimental uncertainty in important input parameters: longitudinal elastic modulus, Poisson’s ratio, static friction coefficient and ultimate tensile strain. The average experimental breaking load of the cable was 190.25 kN (coefficient of variation of 1.74%) and the agreement with the numerical model predictions were good, with an average-value deviation of –1.15%, which is lower than the experimental variations. The simplified analytical model yielded a discrepancy above 10%, indicating that it needs further refinement although much less time consuming than the numerical model. These conclusions were corroborated by statistical analyses (i.e. Kruskal–Wallis and Mann-Whitney).

Keywords
Composite cables; finite element analysis; analytical model; design of experiments; uncertainty quantification

	1×7 CFRP cable	Single CFRP rod
	Breaking load (kN)	$E_{1}$ (GPa)	$ν_{12}$	$S F C$	$ε_{1 t}^{u}$
Average	190.25	141.60	0.28	0.61	1.64%
$σ$	3.31	6.01	0.02	0.05	0.15
CV	1.74%	4.24%	7.14%	8.20%	9.15%

				${\bar{ε}}_{1 t}^{u - σ}$		${\bar{ε}}_{1 t}^{u}$		${\bar{ε}}_{1 t}^{u + σ}$
	Model			Numerical	Analytical	Numerical	Analytical	Numerical	Analytical
Run-1	${\bar{E}}_{1}^{- σ}$	${\bar{ν}}_{12}^{- σ}$	${\bar{S F C}}^{- σ}$	164.27	184.64	180.81	203.23	197.34	221.82
Run-2	${\bar{E}}_{1}^{- σ}$	${\bar{ν}}_{12}^{- σ}$	$\bar{S F C}$	164.39		180.94		197.49
Run-3	${\bar{E}}_{1}^{- σ}$	${\bar{ν}}_{12}^{- σ}$	${\bar{S F C}}^{+ σ}$	164.46		181.01		197.57
Run-4	${\bar{E}}_{1}^{- σ}$	$\bar{ν_{12}}$	${\bar{S F C}}^{- σ}$	164.08	184.55	180.60	203.13	197.12	221.71
Run-5	${\bar{E}}_{1}^{- σ}$	$\bar{ν_{12}}$	$\bar{S F C}$	164.21		180.74		197.27
Run-6	${\bar{E}}_{1}^{- σ}$	$\bar{ν_{12}}$	${\bar{S F C}}^{+ σ}$	164.27		180.81		197.34
Run-7	${\bar{E}}_{1}^{- σ}$	${\bar{ν}}_{12}^{+ σ}$	${\bar{S F C}}^{- σ}$	163.83	184.46	180.33	203.03	196.82	221.59
Run-8	${\bar{E}}_{1}^{- σ}$	${\bar{ν}}_{12}^{+ σ}$	$\bar{S F C}$	163.96		180.46		196.97
Run-9	${\bar{E}}_{1}^{- σ}$	${\bar{ν}}_{12}^{+ σ}$	${\bar{S F C}}^{+ σ}$	164.08		180.60		197.12
Run-10	$\bar{E_{1}}$	${\bar{ν}}_{12}^{- σ}$	${\bar{S F C}}^{- σ}$	171.05	192.81	188.27	212.22	205.49	231.63
Run-11	$\bar{E_{1}}$	${\bar{ν}}_{12}^{- σ}$	$\bar{S F C}$	171.12		188.35		205.57
Run-12	$\bar{E_{1}}$	${\bar{ν}}_{12}^{- σ}$	${\bar{S F C}}^{+ σ}$	171.19		188.42		205.65
Run-13	$\bar{E_{1}}$	$\bar{ν_{12}}$	${\bar{S F C}}^{- σ}$	170.78	192.71	187.97	212.12	205.17	231.52
Run-14	$\bar{E_{1}}$	$\bar{ν_{12}}$	$\bar{S F C}$	170.92		188.12		205.33
Run-15	$\bar{E_{1}}$	$\bar{ν_{12}}$	${\bar{S F C}}^{+ σ}$	170.98		188.20		205.41
Run-16	$\bar{E_{1}}$	${\bar{ν}}_{12}^{+ σ}$	${\bar{S F C}}^{- σ}$	170.58	192.62	187.75	212.01	204.92	231.40
Run-17	$\bar{E_{1}}$	${\bar{ν}}_{12}^{+ σ}$	$\bar{S F C}$	170.64		187.82		205.00
Run-18	$\bar{E_{1}}$	${\bar{ν}}_{12}^{+ σ}$	${\bar{S F C}}^{+ σ}$	170.78		187.97		205.17
Run-19	${\bar{E}}_{1}^{+ σ}$	${\bar{ν}}_{12}^{- σ}$	${\bar{S F C}}^{- σ}$	177.68	200.98	195.57	221.22	213.46	241.45
Run-20	${\bar{E}}_{1}^{+ σ}$	${\bar{ν}}_{12}^{- σ}$	$\bar{S F C}$	177.76		195.65		213.54
Run-21	${\bar{E}}_{1}^{+ σ}$	${\bar{ν}}_{12}^{- σ}$	${\bar{S F C}}^{+ σ}$	177.90		195.81		213.72
Run-22	${\bar{E}}_{1}^{+ σ}$	$\bar{ν_{12}}$	${\bar{S F C}}^{- σ}$	177.46	200.88	195.33	221.10	213.19	241.33
Run-23	${\bar{E}}_{1}^{+ σ}$	$\bar{ν_{12}}$	$\bar{S F C}$	177.61		195.49		213.37
Run-24	${\bar{E}}_{1}^{+ σ}$	$\bar{ν_{12}}$	${\bar{S F C}}^{+ σ}$	177.68		195.57		213.46
Run-25	${\bar{E}}_{1}^{+ σ}$	${\bar{ν}}_{12}^{+ σ}$	${\bar{S F C}}^{- σ}$	177.24	200.78	195.09	220.99	212.93	241.20
Run-26	${\bar{E}}_{1}^{+ σ}$	${\bar{ν}}_{12}^{+ σ}$	$\bar{S F C}$	177.39		195.25		213.11
Run-27	${\bar{E}}_{1}^{+ σ}$	${\bar{ν}}_{12}^{+ σ}$	${\bar{S F C}}^{+ σ}$	177.46		195.33		213.19

	Kolmogorov–Smirnov	Levene	Kruskal–Wallis (for differences between models)	Mann-Whitney	Kruskal–Wallis (for individual parameters)
Experimental	< 0.001	0.017	< 0.001	-	-
Numerical				0.852	1.00
Analytical				0.022	1.00

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[1] * Corresponding author

$E_{1}$ = 141.6 GPa (±6) ^* * Experimentally measured.	$G_{12}$ = 5.3 GPa	$ν_{12}$ = 0.28 (±0.02)*
$E_{2}$ = 7.6 GPa	$G_{13}$ = 5.3 GPa	$ν_{13}$ = 0.28
$E_{3}$ = 7.6 GPa	$G_{23}$ = 4.7 GPa	$ν_{23}$ = 0.47