A Review of Classical Fiber Microbuckling Analytical Solutions for use with Elastic Memory Composites

Francis, William; Lake, Mark S.; Mayes, J. Steven

doi:10.2514/6.2006-1764

Cited by 19 publications

(28 citation statements)

References 9 publications

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“…However, this study focuses on postmicrobuckled behavior and the model does not apply for small deformations. Substituting those test parameters [7] into Equation (16) deduced in this study, the microbuckling wavelength of the continuous-carbon-fiber/resin EMC laminate is about 0.72 mm, which is comparable with the test result, 1 mm. Meanwhile, the expressions of the critical microbuckling stress, Equation (18), and strain, Equation (19), derived from the expression of microbuckling wavelength, Equation (16), in the proposed model are reasonable and intuitively correct.…”

Section: Introductionsupporting

confidence: 76%

“…The main mechanism that allows much higher folding strain without damage is due to microbuckling, and post-microbuckling response of the compressively loaded fibers during bending, which have been confirmed by tests [5][6][7]. For example, although the ultimate strain of high-performance carbon fibers is usually lower than 1%, continuous-carbon-fiber-reinforced EMC laminate can receive more than 5% equivalent bending strain.…”

Section: Introductionmentioning

confidence: 81%

“…The solution and the intersection point of the straight line given by Equation (1) and the curve given by Equation (4) By combining the matrix strain energy given by Rosen's solution for shear instability-mode microbuckling composite [9] with Timoshenko's elastic foundation energy [10], a suitable model and solution is proposed to determine the critical wavelength and critical microbuckling strain of the fibermicrobucking in EMC laminate under pure bending. Based on the laboratory observations that the same wavelength of sinusoidal-like and in-plane microbuckling exist in the EMC laminate under pure bending [6][7], the following simplified assumptions are applied: all fibers display sinusoidal-like microbuckles with the same mode number; the microbuckling mode is recognized as a 1D mode instead of 3D mode since no out-of-plane microbuckle is observed in tests; only shear microbuckling is identified as the available tests exhibit that it is the dominated mode for EMC laminates under bending. Fig.…”

Section: Introductionmentioning

confidence: 99%

“…The theoretical buckled shape for shear mode is a single half sine function along the length of the specimen of EMC laminate under bending. However, the test specimen is 250 mm in length and the fibers have a normal wavelength of around 1 mm [7]. In addition, the critical microbuckling wavelength predicted by the extension mode is about 0.09 mm.…”

Section: Introductionmentioning

confidence: 99%

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Transition Curvature of Soft Matrix Composite Laminates during Bending

Xiong

Song

et al. 2016

MATEC Web Conf.

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Abstract.As an Elastic memory composite (EMC) laminate is bent, the prebuckled plate theory is valid until the transition curvature at which point the postbuckled solution becomes effective. This is the point at which microbuckling is predicted to occur. From the point onward, EMC laminate follows the postbuckled solution. In this paper, a solution of the transition curvature is proposed by combining matrix shear energy with Timoshenko's elastic foundation energy. By comparing with the intersection point of the straight line given by the prebuckled plate theory and the curve given by the postbuckled solution, the solution can be used to predict the point at which microbuckling is predicted to occur.

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Section: Introductionsupporting

confidence: 76%

Section: Introductionmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Transition Curvature of Soft Matrix Composite Laminates during Bending

Xiong

Song

et al. 2016

MATEC Web Conf.

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“…Turning to the behavior of thin sheets of uniaxial carbon fibers embedded in a soft matrix, analytical expressions for estimating the wavelength and amplitude of the microbuckled fibers were obtained by Francis et al [22,23]. These authors assumed that the buckles can be described by the sine function…”

Section: Introductionmentioning

confidence: 99%

Failure of Carbon Fibers at a Crease in a Fiber-Reinforced Silicone Sheet

Jiménez

Pellegrino

2012

Journal of Applied Mechanics

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Thin sheets of unidirectional carbon fibers embedded in a silicone matrix can be folded to very high curvatures, as elastic microbuckles with a half-wavelength on the order of 1 mm decrease the maximum strain in the fibers near the compression surface. This paper shows that probabilistic failure models derived from tension tests on individual fibers can be used to predict accurately the value of the outer surface curvature of the sheet, at which a small percentage of fibers break when a crease is formed in the sheet. The most accurate results are obtained by using a strain-based Weibull distribution of the failure probability in tension.

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Theoretical analysis of the deformation of SMP sandwich beam in flexure

Wang

2011

Arch Appl Mech

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Shape memory polymers (SMPs) can have a large frozen strain but with a very small recovery stiffness in comparison with shape memory metals or ceramics. To provide more deployable stresses for the application of actuators, sandwich beams consisting of a SMP core and two thin metallic skins were considered. The packaging behaviors of two types of SMP sandwich beams, aluminum/SMP/aluminum and steel/SMP/steel, were discussed. Due to the high compliance of SMP core on packaging condition that the testing temperature is above the activation temperature of the material, buckling and post-buckling are the essential deformation mechanisms of SMP sandwich beams under bending. Theoretical solutions were derived in studying such non-linear behaviors, including the initiation of critical buckling, post-buckling response, and final failure modes. Systematic parameter's analyses, e.g., buckling half-wavelength, amplitude, location of the neutral-strain surface in different packaging curvatures, were also presented.Keywords Shape memory polymer · Sandwich structure · Shape recovery · Buckling · List of symbols z m thickness of metallic skin z e thickness of SMP epoxy core z t thickness of tensioned SMP core z c thickness of compressed SMP core z t thickness of tensioned metallic skin z c thickness of compressed metallic skin ε eff effective strain E eff effective modulus of buckled skin ε z strain of SMP core γ xoz shear strain of SMP core w buckling displacement of metallic skin w e displacement of SMP core E m Young's modulus of metallic skin E e Young's modulus of SMP epoxy core G m shear modulus of metallic skin G e shear modulus of SMP epoxy core l length of SMP sandwich beam b width of SMP sandwich beam a buckling magnitude of metallic skin λ buckling wavelength of metallic skin m buckling mode number of metallic skin EI flexural stiffness of metallic skin ρ curvature radius M applied bending moment z ns distance from geometric midplane to neutral-strain surface T virtual work applied on the compressed region U m c compressed strain energy in unbuckled metallic skin U m b strain energy in buckled metallic skin U e strain energy in SMP epoxy core U S xoz shear strain energy of SMP core in the x − z plane U T z tensioned/compressed strain energy of SMP core along length direction

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A Review of Classical Fiber Microbuckling Analytical Solutions for use with Elastic Memory Composites

Cited by 19 publications

References 9 publications

Transition Curvature of Soft Matrix Composite Laminates during Bending

Transition Curvature of Soft Matrix Composite Laminates during Bending

Failure of Carbon Fibers at a Crease in a Fiber-Reinforced Silicone Sheet

Theoretical analysis of the deformation of SMP sandwich beam in flexure

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