Anisotropic Materials Research Articles

Acoustic Wave Velocities in Bridge Steels and the Effects on Ultrasonic Testing

Ultrasonic testing is utilized to ensure weld quality during the fabrication of steel bridges by identifying discontinuities that are classified as either acceptable or rejectable. The classification of a discontinuity can be affected by differences in the acoustic properties of the material under test and the reference standard used for calibration. Differences in wave velocity affect the refracted angle and amplitude of refracted shear waves. As a result, indications can be missed or incorrectly classified, or incorrectly located in the material. The objective of this research study was to characterize the acoustic wave velocities in a sample of contemporary steels to better understand the range over which velocities may vary for common steels. To address this objective, a series of velocity measurements have been conducted for shear waves propagating through different directions in steel plates of different strengths and reported manufacturing processes. The study also examines the loss of signal amplitude that results from changes in the refracted angle of shear waves used for the inspection of welds. Beam splitting that may occur in anisotropic materials and the potential impact on signal amplitudes is also presented. It was shown in the research that relatively small differences in velocity between the material under test and the reference standard cause a loss of sensitivity of the test. Data presented in the paper documents wave velocity and anisotropic ratios for a population of contemporary bridge steels used for the fabrication of steel bridges and an assessment of how velocity differences affect the amplitude of reflected shear waves.

Multiprogrammable Anisotropic Soft Material via Magneto‐Orientation of Ferromagnetic Nanoplates

AbstractAnisotropic materials featured with ordered arrangement of sub‐structures are ubiquitous in living organisms, and possess rapidly increasing relevance to emerging technologies in smart materials, soft robotics, flexible displays, and biomedicines. However, the integration and programming of multiple properties into anisotropic materials, which endow themselves with extended intrinsic capabilities and utilities, still remain a challenge. Herein, we report a multi‐programmable anisotropic material by embedding ferromagnetic two‐dimensional nanoplates into hydrogel matrix. The nanoplate exhibits not only a disc‐like non‐isotropic shape, but also an intrinsic easy magnetization axis perpendicular to its basal plane. Using a directional external magnetic field, we can precisely control the orientation of nanoplates inside hydrogel precursor solution and then fix them via photolithographic polymerization, leading to the fabrication of anisotropic hydrogel with on‐demand ordered alignment of nanoplates. Such deliberate arrangement of nanoplates brings in extraordinary optical properties due to birefringence, enabling us to encrypt pattern information into hydrogel materials that is only visible under polarized light. Soft actuators with programmable optical, mechanical and magnetic properties are engineered, which allow to encode diverse deformation and locomotion modes, determine the actuation sites, and monitor the sub‐structural anisotropy all simultaneously, opening new avenues for the design of anisotropic soft materials.

Ray and energy-flux velocities at a contact of two viscoelastic anisotropic materials

Summary A g*-Hamiltonian method for tracing real rays was developed that can handle cusps and triplication of quasi-shear wave in a general viscoelastic anisotropic medium. We demonstrate that the g*-Hamiltonian method can produce homogeneous ray-velocity vectors (with parallel real and imaginary parts) and the slowness vectors of reflected and transmitted waves at the interface based on the real Snell's law (RSL), which constrains only the continuity of the real parts of the slowness vectors, or the real slowness direction (RSD) method, which ignores the inhomogeneous component of the slowness vector. These methods are based on the characteristic lines with different Hamiltonians. Our research indicates that these methods are limited to pre-critical incidence ranges. Moreover, we derived a complex energy velocity vector (energy flux velocity) expression, which is always homogenous. We found that directions of corresponding energy velocity calculated with complex Snell's law (CSL) at a contact of two viscoelastic anisotropic materials well match the solutions of the RSL and RSD methods for all R/T waves except post-critical incidence, whereas the RSL and RSD methods fail to obtain homogenous ray velocities. The RSL and RSD methods result in discrepancies in the ray quality factor, R/T coefficients, and energy ratios, especially for post-critical incidence. However, the exact critical angle determined by the RSD method approximates the ‘critical’ angle for anelastic/inhomogeneous waves, which was a previous challenge. Our calculations suggest that the energy velocity and energy quality factor obtained with the CSL method can be used for real ray tracing at the interface of viscoelastic anisotropic media, and the complex energy flux velocity vector is always exactly homogeneous. For the post-critical incidence, the RSL and RSD methods fail because the ray quality factor drastically changes from the infinite down to near 2, which contradicts homogeneous ray velocity in elastic anisotropic materials. However, the energy quality factor for the elastic-anisotropic material is all infinite, even for post-critical incidence, which is correct. We also show that the CSL method has the same efficiency as the RSD method.

ANALYSIS OF SH-WAVES IN ANISOTROPIC FIBER-REINFORCED MEDIUM OVER LINEARLY VARYING INHOMOGENEOUS SUBSTRATE UNDER NON-LOCAL ELASTICITY

An analytical technique employing the variable separable method has been used in an attempt to precisely grasp and assess the impact of the property non-local elasticity upon the wave transmission response of an anisotropic fiber-reinforced material embedded over a semi-infinite, inhomogeneous medium that changes linearly. As depth increases, the stiffness and density of a semi-infinite substrate are believed to alter linearly. Availing the Whittaker function, a relation about dispersion has been acquired to analyze the response of SH waves. The visual representation depicts a significant influence of non-local elasticity on the propagation of SH-wave modes. Special cases have been found assessing the concurrency of the model with the original form equation of Love wave. The effects of non-locality, fiber-reinforcement parameters, and inhomogeneity parameters carry implications in designing and gradation of material characteristics some important parameters on the wave characteristics of the studied model.

Damage characterization and modelling of FRP laminated composites subjected to external edge-on impact

This paper presents both experimental and numerical investigations into the edge-on impact behavior of T700/YPH307 composite laminates with varying lay-up designs and impact energy levels. Various non-destructive testing techniques, including visual inspection, ultrasonic C-scanning and X-ray computed tomography (CT), were used to detect the post-impact damage status and further reveal its 3D spatial distribution. A continuum damage mechanics (CDM) model, incorporating in-plane shear nonlinearity, fracture plane angle within anisotropic materials, as well as fiber kinking failure in longitudinal compression, was established using an explicit solver. Detailed comparison of the experimental and numerical results was conducted in mechanical response curves and failure mechanisms, where a good agreement was observed. Parameter analyses on the in-situ strengths and the friction coefficient were also performed, offering guidelines for the edge-on impact modelling. Failure mechanisms induced by edge-on impact typically exhibit two distinct features: a highly localized debris wedge, which can be regarded as a trigger in the subsequent occurrence of damage, and the bending fracture of the outer plies resulting from the wedge effect during the oscillating stage of an impact force plateau. Besides, higher impact energy exacerbated internal damage, while the influence of the lay-ups was relatively limited.

Phase-field approach for precise fracture tracking in anisotropic rocks: Integrating orthotropy-based energy decomposition and two-fold symmetric fracture toughness

Rock formations are known to exhibit material anisotropy, both in terms of elastic and fracture properties. This means that the fracture path in such formations is not a priori known but rather a complex unknown that requires robust numerical techniques to predict accurately. In this context, the phase-field model is considered particularly effective, provided that certain physical considerations are carefully adjusted to align with the physics of the problem. While addressing elastic anisotropy is well-established, the tension–compression asymmetry necessary to inhibit crack interpenetration in phase-field fracture models needs to account for the specific material anisotropy. Additionally, to accurately capture crack propagation, it is critical to simultaneously account for orientation-dependent fracture toughness in such materials. To address this, the present study employs an anisotropic phase-field model that integrates the generalized spectral decomposition proposed in the literature for orthotropic materials with a two-fold symmetric fracture toughness, to predict the fracture trajectories in rock-type samples under fixed mixed-mode loading ratios. While each of the two aspects has primarily been applied to model orthotropic plates under simple tensile and shearing loading conditions in the literature, here we study their applicability in complex loading scenarios. To this end, the experimental data from notched semi-circular specimens of Grimsel Granite undergoing complex mixed-mode loading obtained in our previous work is considered. We focus on two given mode-mixity ratios and perform numerical studies. Our results emphasize the importance of considering this generalized decomposition for phase-field modeling of fracturing in rock-type materials, particularly under loading conditions where the crack might otherwise be unrealistically driven into the compressive region. Although certain features are well captured by considering anisotropy in elasticity alone, our findings demonstrate that incorporating a two-fold symmetric fracture toughness proves to be advantageous for more precise tracking of the fracture path.

Unified non-hourglass formulation for total Lagrangian SPH solid dynamics

AbstractThe persistence of hourglass modes poses a significant numerical instability issue in total Lagrangian smoothed particle hydrodynamics (TLSPH) solid dynamics, especially when dealing with substantial deformations, regardless of material properties. However, existing hourglass control methods have shown effectiveness only within limited applications. Thus far, a comprehensive solution capable of addressing hourglass issues across a wide range of material models, including elasticity, plasticity, and anisotropy, remains elusive. In this study, we introduce a unified TLSPH formulation grounded in volumetric-deviatoric stress decomposition, aimed at fundamentally mitigating hourglass modes in general simulations. Different conceptually from previous approaches using stress points or extra viscous or hourglass-control stresses within the momentum equation, our formulation is based on the weighted average of a standard but hourglass-prone formulation and an essentially non-hourglass formulation for elastic materials, employing a single limiter to dynamically adjust the weighting between the two formulations. Crucially, the dimensionless characteristic of the formulation enables seamless handling of complex material models. To validate the effectiveness of our formulation, we conduct simulations across a range of benchmark cases involving elastic, plastic, and anisotropic materials. To illustrate its versatility, we apply the formulation to simulate a complex scenario involving viscous plastic Oobleck material, contacts, and very large deformation. Our work addresses a critical gap in TLSPH simulations by offering a unified approach to mitigate hourglass modes, enhancing the reliability and accuracy of simulations across diverse material models and complex scenarios.

High Temperature, Isothermal Growth Promotes Close Packing and Thermal Stability in DNA-Engineered Colloidal Crystals.

We report a strategy to accelerate the synthesis and increase the crystallinity of colloidal crystals (CCs) engineered with DNA. Specifically, by holding the DNA-modified Au particle building blocks above the Tm of the DNA bonding elements (i.e., free from the particles), but slightly below the Tm of the anticipated CC during the assembly process, crystallinity is increased, and enthalpically favored phases with high degrees of facet registration are observed. We studied the utility of this approach with systems for which the commonly adopted slow-cooling approach yielded primarily amorphous aggregates. In particular, we used it to synthesize high-volume fraction CCs from large (80 nm) anisotropic nanoparticles (cubes and rhombic dodecahedra) with short (<14 nm) DNA designed to restrict the degrees of freedom for the DNA bonds and maintain the anisotropy of the particle building block. Small-angle X-ray scattering and electron microscopy studies show that the crystalline phases synthesized via this method are more thermally stable than their corresponding aggregate phases, likely due to an increased number of DNA-DNA bonds between particles. Crystal size tunability (between 0.5 and 15 μm edge lengths) and epitaxial growth were demonstrated using this strategy by modulating the NaCl concentration in tandem with previously synthesized CC nuclei. Taken together, this isothermal strategy demonstrates how to deliberately crystallize a wide variety of anisotropic colloidal materials and expands the phase space accessible to nanoparticles modified with DNA.

Experimental characterization of the effective acoustic properties of anisotropic porous materials via free-field measurements

Porous media are commonly described as effective isotropic fluid materials, such that their acoustic properties can be adequately determined from their bulk modulus and dynamic density. Most acoustic absorbents, however, possess a marked anisotropy, which influences their acoustical behavior and the parameters necessary to deduce it. Specifically, the influence of anisotropy translates into a full symmetric density tensor (in place of a scalar). This study presents a method for retrieving the bulk modulus and all six components of the density tensor of a layer of porous material from reflection coefficients measured in free field with an array of microphones. The procedure consists in expressing the sound field measured in the vicinity of the layer as a superposition of plane waves, from which the surface impedance and the reflection coefficient are reconstructed. The reflection properties, as well as the pressure at the rigid backing interface, are estimated for various source positions (i.e., various angles of incidence) and an inverse problem is formulated to infer the effective fluid parameters. The validity of the method is examined experimentally on a manufactured porous material, and the resulting fluid parameters compared with experimental results obtained from reflection and transmission coefficients measured in an impedance tube.

High‐performance visible and near‐infrared dual‐band photodetector based on anisotropic 2D NbS3 with perpendicularly reversed polarization behaviors

AbstractDual‐band photodetectors exhibit considerable advantages in target discrimination and navigation compared to single‐band devices in complex circumstances. However, it remains a major challenge to overcome the limitations of traditional devices in terms of their integration with multiple light‐absorbing layers and complicated optical components. In this study, a visible and near‐infrared (NIR) dual‐band polarimetric photodetector with a single light‐absorbing layer is constructed by utilizing the distinctive conversion of linear dichroism (LD) polarity in two‐dimensional niobium trisulfide (NbS3). The NbS3 photodetector exhibits selective detection behaviors in the visible and NIR bands, in which by switching the polarization angle of the incident light from 0° to 90°, photocurrent decreases in the visible region, and increases in the NIR region. Specifically, the degrees of linear polarization of photocurrent are 0.59 at 450 nm and −0.47 at 1300 nm, respectively. The opposite photoresponse in the visible and NIR bands of the photodetector significantly enhances the dual‐band information recognition. Therefore, clear visible and NIR dual‐band polarimetric imaging is accurately realized based on the NbS3 photodetector taking advantage of its fast response speed of 28 μs. Such anisotropic materials, with unique LD conversion features, can facilitate selective modulation between the visible and NIR spectral ranges and promote the development of next‐generation multi‐dimensional photodetection for various applications, including com/puter vision, surveillance, and biomedical imaging.image

An anisotropic eigenfracture approach accounting for mixed fracture modes in wooden structures by the Representative Crack Element framework

Finite Element analysis of anisotropic fracture phenomena in wood is a challenging task, particularly when dealing with intricate loading scenarios and mode-specific behavior. The appeal of energetically motivated approaches, such as the eigenfracture method, is that they enable simulation of fracture without prior knowledge of the crack path. The promising eigenfracture method has shown good numerical performance for isotropic materials, and this contribution showcases its application to anisotropic materials. Wood is one such anisotropic material and in this manuscript, the directional dependence of both elasticity and fracture evolution are incorporated into the eigenfracture approach. Further, the eigenfracture approach is used in conjunction with Representative Crack Elements (RCE), which permit accurate modeling of physical crack deformations. The governing equations are systematically derived and implemented into the Finite Element framework. By representative numerical examples, some advantages over the alternative phase-field method are demonstrated. Another highlight of this work is that it is possible to provide a realistic ratio of the energy release rates parallel to and perpendicular to the fiber direction in order to achieve physically accurate crack patterns. Additionally, the calculation effort is reduced, because the unknowns required to determine the crack kinematics can be solved analytically at the material level, a feature that also enables parallelization.

Planar structured materials with extreme elastic anisotropy

Designing anisotropic structured materials by reducing symmetry results in unique behaviors, such as shearing under uniaxial compression. While rank-deficient materials such as hierarchical laminates have been shown to exhibit extreme elastic anisotropy, there is limited knowledge about the fully anisotropic elasticity tensors achievable with single-scale fabrication techniques. No established upper and lower bounds on anisotropic moduli exist. In this paper, we estimate the range of anisotropic stiffness tensors achieved by single-scale two-dimensional structured materials. We first develop a database of periodic anisotropic single-scale unit cell geometries using linear combinations of periodic cosine functions. The database covers a wide range of anisotropic elasticity tensors, which are then compared with the elasticity tensors of hierarchical laminates. We identify the regions in the property space where hierarchical design is necessary to achieve extremal properties. We demonstrate a method to construct various 2D functionally graded structures using this cosine function representation. These graded structures seamlessly interpolate between unit cells with distinct patterns, allowing for independent control of several functional gradients, such as porosity, anisotropic moduli, and symmetry. When designed with unit cells positioned at extreme parts of the property space, these graded structures exhibit unique mechanical behaviors such as selective strain energy localization, compressive strains under tension, and localized rotations.

Eulerian rates of elastic incompatibilities applied to size-dependent hardening in finite torsion

Measures of rates of elastic incompatibilities are developed within an Eulerian framework for finite-deformation response of anisotropic elastic-inelastic materials. Such framework relies on the evolution of microstructural vectors. It is emphasized that the rates of incompatibilities, here denoted as Rij, depend on the constitutive equation for the rate of inelasticity. For small strains and rotations, Rij are equal to the negative of the components of the rate of Nye-Kröner’s dislocation density tensor. In contrast to these small strain components, each Rij is invariant under superposed rigid body motions such that it can be used independently in the constitutive equations to describe the material behavior. Specifically, in this work, Rij provide a size-dependent enhancement to hardening that can increase or decrease during loading history, modeling the generation and annihilation of densities of geometrically necessary dislocations in metal plasticity. The application to the finite-deformation torsion of thin wires demonstrates the potential of this approach and the importance of the constitutive equation for the plastic spin rate both on the rotations of the microstructural vectors and on the predicted size-effect.

A critical appraisal of the Hashin failure criterion

The Hashin criterion is one the most popular failure criteria for fibre reinforce composites. It is critically appraised in this paper. The most significant feature of the criterion is failure modes introduced and the assumption that failure is determined by the traction on the failure plane. For this assumption, there has never been any justification provided in the literature, except the available arguments in the Mohr criterion, where the concept of plane failure as opposed to point failure was first introduced based on this assumption. However, the arguments there were applicable only to isotropic materials and, even so, they are not without exceptions. As contradictions to the assumption in the context of composite failure, three relatively simple cases have been considered in this paper, supported by physical evidence. In each case, failure is observed in a plane on which traction vanishes completely, to which the failure cannot be attributed. The assumption is therefore unfounded both theoretically and physically for anisotropic materials, which dismisses the validity of the Hashin criterion in turn.

Constitutive modelling and wave propagation through a class of anisotropic elastic metamaterials with local rotation

Elastic metamaterials are typically periodic materials possessing unit cells endowed with engineered architecture much smaller than the typical phenomenological length scale. The development of continuum models capable of accurately representing the effects of this aforementioned architecture is extremely challenging, and hence a sparsely developed area. This paper develops a novel 2-D continuum model capable of capturing the dynamic behaviour of a class of anisotropic elastic metamaterials with local rotational elements in the long wavelength limit. A constitutive relation incorporating these local rotational effects is proposed, and ratified using a representative discrete model using linear Hookean springs and identical rigid disks. The new continuum model is used to generate a dispersion relation for harmonic plane waves propagating in an arbitrary direction, which is subsequently compared to the dispersion behaviour of the original discrete model. The general behaviour of this continuum when subjected to 2-D planar harmonic wave propagation in the anisotropic medium is then analyzed, with specific attention given to the effect of material anisotropy and wave propagation direction. This work is the first of its kind to create a new continuum model of a class of anisotropic elastic metamaterials with local rotational effects.

자계 이방성 축 방향에 따른 안테나 공진 주파수 특성

The main theme of the 2024 Mobile World Congress (MWC), held annually in Barcelona, Spain, is ‘5G and Beyond.’ Extensive research and activity focus on 6G (IMT-2030) technology, which is expected to become the core infrastructure of the mobile industry by 2030, representing the future of wireless communications. This necessitates the support of more wireless frequency bands for terminals to be compatible with the upcoming Beyond 5G (B5G) and 6G technologies. The antenna mounting space for B5G wireless communication, with various form factors for hardware, such as smartphones, smartwatches, and smart rings, is limited, as these devices become increasingly slimmer and lighter. Several methods have been studied to reduce antenna size while maintaining performance in a limited space. Representative examples include integrated-structure, metamaterial, and magnetodielectric antennas. In this study, it is analyzed for the effect of the resonance frequency characteristics of antennas based on the arrangement direction of the anisotropic material in the limited antenna mounting space of communication terminals. Aiming to reduce antenna size in the B5G era, it is proposed for the necessity of optimal design that focuses on the axial direction of the magneto-dielectric materials when designing antennas using anisotropic materials for antenna miniaturization.

DISPERSION OF LAMB WAVES IN MULTILAYER STRUCTURES

Low cost, the possibility of online monitoring and high sensitivity distinguish the method of structural monitoring using Lamb waves from other available methods. Structural analysis based on Lamb waves in heterogeneous materials requires fundamental knowledge of the behavior of Lamb waves in such materials. This basic knowledge is critical for signal processing in determining possible damage that can be detected by the propagating wave. Recently, Lamb wave methods have been used to simultaneously survey large areas of composite structures. However, such methods are more complex than traditional ultrasonic testing because Lamb waves have dispersive characteristics, namely, the wave speed varies depending on the frequency, modes and thickness of the plates. Experimentally measured group velocities of Lamb waves in composite materials with anisotropic characteristics do not coincide with theoretical group velocities, which are calculated using the dispersion equation of Lamb waves. This discrepancy arises because in anisotropic materials there is an angle between the direction of the group velocity and the direction of the phase velocity. This work investigates the propagation characteristics of Lamb waves in composites, focusing on group velocity and characteristic wave curves. For symmetric laminates, a robust method is proposed by imposing boundary conditions on the mid-plane and top surface to separate symmetric and antisymmetric wave modes. The dispersive and anisotropic behavior of Lamb waves in two different types of symmetrical laminates is theoretically studied in detail. The dispersion of Lamb waves was studied for 10 symmetric and asymmetric modes. It is shown that only fundamental modes are not characterized by a cutoff frequency, which indicates the interaction of fundamental modes with composite layers in the low-frequency range. A high level of group velocity dispersion was discovered for the SH0 and S0 modes. It is concluded that in isotropic laminates, dispersion is characteristic of symmetric modes. It is shown that the frequency dependence of the group velocity of Lamb waves of laminar composites can be represented in polynomial form.

Mechanics of Materials: Multiscale Design of Advanced Materials and Structures

Materials can now be designed and architectured like structural components for targeted mechanical and physical properties. Structures and microstructures should not be studied independently and their design will benefit from a multiscale approach combining nonlinear continuum mechanics approaches and physical descriptions of elasticity, viscoplasticity, phase transformations and damage of microstructures, at various scales. The aim of the workshop was to gather outstanding junior and senior researchers in the various branches of mathematics, physics and engineering sciences suited to address the question of design of materials and structures by means of multiscale discrete and continuum approaches to their constitutive behavior. Examples include atomic or macroscopic lattices, random or periodic cellular materials, smart materials like shape memory alloys, 3D woven composites, acoustic and electromagnetic metamaterials, etc. Modern continuum mechanics relies on sophisticated constitutive laws for anisotropic materials exhibiting elastoviscoplastic behavior, still a field of intense research with new mathematical concepts. In particular size-dependent properties are addressed by resorting to generalized continua such as gradient or micromorphic and phase field models. The latter are attractive for the simulation of microstructure evolution coupled with mechanics, due to thermodynamic and metallurgical processes and damage. Scale transition and homogenization methods for continuous and discrete systems are required for the determination of effective material and structural behavior. Metamaterials are architectured materials specifically designed to achieve certain propagation and dispersion properties of elastic and plastic waves. Optimization strategies for the design of optimal architectures are involved in the design process. Target functions for optimization are now based on multicriteria (stiffness, strength, thermal expansion, transport properties, anisotropy etc.).

Systematization of the application of polymer composite materials in the design of bridge structures

Background. This study systematizes the principles of using polymer composite materials in bridge structure design, outlining the fundamental principles for calculating load-bearing structures of bridge spans featuring these materials. Aim. The goal is to enhance the strength and durability of bridge spans during construction and maintenance, while optimizing costs through the use of polymer composite materials. Materials and Methods. The research employs a modern approach to bridge structure design, utilizing mathematical statistics for experimental data analysis and numerical methods for calculating bridge structures using nonlinear deformation models of anisotropic materials. Results. Developed principles for designing bridge spans with polymer composite elements include methods for strengthening and reinforcing concrete bridge structures. These methods account for operational factors such as long-term constant and temporary loads, low and elevated temperatures, as well as methods for designing all-composite spans pedestrian and road bridges Conclusion. The principles of designing bridge spans with elements made of polymer composite materials have been introduced into the practice of transport construction in the Russian Federation. The technical and economic efficiency of using polymer composite materials in bridge structures of transport infrastructure has been confirmed.

Analysis of compact tension specimens with deflected cracks for orthotropic materials

Anisotropic materials, such as alloy, wood and fiber-reinforced composites, are widely used in load-bearing components. Accurately obtaining its fracture performance is crucial for safety assessment. However, existing testing methods based on compact tension (CT) specimen have not taken into account material anisotropic characteristics and crack deflection. In this work, the systematic finite element analysis (FEA) was conducted for CT specimens with deflected cracks made of orthotropic materials. A wide range of geometric (crack deflection angle, β, and ratio of crack length to width, ap/W) and orthotropic material (λ and ρ) parameters were discussed. Complete solutions of the stress intensity factor (KI and KII) and load-line compliance (C) were determined for the first time. The results showed that the geometric dimensions and material parameters have a significant coupling influence on the fracture parameters. The influence of the λ is generally greater than that of the ρ. Changes of material parameters can make fracture parameters’ dependence on β vary. The variation of β and ap/W could enlarge or minish even dismiss the impact of λ and ρ. In addition, to further verify the importance of the obtained fracture parameters, the CT fracture tests of carbon fiber-reinforced epoxy resin under various orientations were conducted. The solutions will promote the optimization of the fracture toughness testing standards for CT specimens made of anisotropy materials.