Modified Beam Theory Research Articles

Fracture properties of bamboo fibrous composites: A systematic review

As a fast-growing grass, bamboo has received a great deal of attention due to the excellent mechanical performance. The unique properties of bamboo come from its natural composite structure - a kind of natural fiber reinforced composites, which is composed of bamboo fibers (reinforcement) and parenchyma tissue (matrix). Based on raw bamboo, man-made bamboo fibrous composites such as engineered bamboo and bamboo fiber reinforced polymeric composites have emerged. These materials eliminate some inherent shortcomings of bamboo, which can provide more stable material performance and achieve dimension alteration according to requirements. All of these bamboo fibrous composites have orthotropic structure, the mechanical properties of which in the longitudinal direction far exceed that in the transverse direction, and the tensile strength and compressive strength can reach 111–114.8 and 104.7–115.7 MPa respectively. Besides, the interfacial zone between fiber and matrix is weak, in which some defects are usually existed, such as micro-cracks and adhesive voids. As a result, cracks in the composites are inevitable, which are easy to extend in the longitudinal direction and result to fracture failure. Consequently, fracture studies become necessary for evaluating the crack-resistance ability of bamboo fibrous composites. This paper systematically introduces the previous research works on the fracture properties of bamboo fibrous composites. Firstly, this paper summarized the test methods for different fracture modes including Double cantilever beam (DCB), Single-edged notched beam (SENB), Compact tension (CT), etc., meanwhile the corresponding calculation theories such as Compliance calibration (CC), Modifed compliance calibration (MCC) and Modified beam theory (MBT) are also elucidated. Subsequently, the fracture behaviors and mechanisms of various bamboo fibrous composites are analyzed, in which the fracture parameters and crack-resistance capabilities are compared. In addition, considering the limitations of current research, the future research in need on the fracture properties of bamboo fibrous composites are discussed, the conclusion can be used in providing important reference for the safety evaluation of bamboo fibrous composites.

Modified double cantilever beam test method for mode-I energy release rate of elastic adhesive layers

This study proposes a Mode I double cantilever beam (DCB) test method for debonding thick elastic adhesive layers. The approach integrates Bernoulli–Euler beams connected via spring elements akin to Winkler’s foundation. Energy release rate determination considers crack length correlation with elastic deformation in the crack-front region, accounting for both beam rotation and lateral movement. Evaluation of Ti6Al4V samples bonded with FM 309 adhesive revealed higher initial energy release rates with the conventional beam theory and conservative values with the modified beam theory. The proposed method offered improved consistency, and less conservative energy release rate values compared to the modified theory.

An experimental and analytical study of mode I fracture and crack kinking in thick adhesive joints

This study investigates the fracture behavior of thick adhesive joints manufactured with composite adherends and bonded with an epoxy-based structural adhesive common to the wind turbine industry. For that purpose, double cantilever beam specimens with an adhesive thickness of approximately 10 mm and different pre-crack lengths are manufactured and tested under mode I loading. Analytical approaches are compared to assess the energy release rate, including the simple beam theory, modified beam theory, compliance calibration method, and beam on an elastic and elastic-plastic foundation. In order to evaluate the applicability of the analytical approaches, an in-situ measurement method based on Digital Image Correlation is also employed to determine the energy release rate of the thick adhesive joints. The crack propagation angle is determined theoretically using the second-order crack kinking theory. A good correlation is observed between the theoretical predictions and experimental results. Furthermore, it is demonstrated that due to the T-stress, the crack tends to deviate from the middle of the joint and propagate towards the interface. By comparing different data reduction methods to evaluate the energy release rate of thick adhesive joints, recommendations for their fracture analysis are made, pinpointing the beam on an elastic and elastic-plastic foundation as the most suitable model.

Characterisation of fatigue delamination growth in plain woven hybrid laminated composites subjected to Mode-I loading

Effect of similar and dissimilar crack plane interface configuration on fatigue delamination growth in plain woven hybrid composite laminates under Mode-I has been investigated. Constant displacement amplitude fatigue testing with displacement ratio of 0.1 was carried out on 3 configurations of plain woven glass/carbon epoxy composite laminates. A power law like fit between recorded delamination length and corresponding cycle was used to predict crack length for each of the cycle. Delamination growth rate,da/dN is computed by differentiating the expression of power-law like fit.The obtained crack growth rate for each of the specimens were plotted with respect to two normalised functions, G^Imax=GImax(a)/GIR(a) where GImax is maximum mode-I energy release rate and GIR(a) is the interlaminar fracture toughness resistance and ΔG^Ieff=G^Imax-G^Imin2 as crack driving parameters computed on the basis of Modified Beam Theory (MBT) and Valvo’s mode partition method (MPV) are used in Paris relation to quantify delamination propagation. It is observed that the exponent values predicted by MBT method for G^Imax is lower as compared to ΔG^Ieff. Whereas, exponent values predicted for G^Imax is higher as compared to ΔG^Ieff predicted by MPV method. The higher the exponent value, the higher is the sensitivity of the model leading to uncertainties in the crack growth prediction. Also, it is to be noted that cyclic loading effect is when both GImax and GImin is considered, the use of ΔG^Ieff as crack driving parameter to quantify delamination propagation is justified. Secondly, MBT method does not account for the mode-mixity arising due to hybrid material configuration as in the case of Local Symmetry Fatigue (LSF) and Asymmetry Fatigue (ASF) specimens. Hence, results in higher exponent as compared to MPV method. On the other side, the G^Imax and ΔG^Ieff computed on the basis of MPV method is the pure Mode-I component deduced from the total energy release rate of mode-mixity.The equations of curve fitting is very much the same for Simple Symmetry Fatigue (SSF) specimens indicating that MBT and MPV methods predict pure Mode-I behaviour for symmetric configuration for delamination growth under fatigue Mode-I loading. From the composite laminate configuration point of view, LSF specimens have higher exponents as compared to ASF and SSF specimens indicating, local symmetry configuration laminates are highly sensitive to the small uncertainties and results in unstable crack growth.Comparison of results of all hybrid composite laminates shows that the normalised functions of G^Imax and ΔG^Ieff as crack driving parameters computed on the basis of MPV method is able to capture the effect of interlayers and stacking effect on the delamination growth in hybrid plain woven composites in fatigue loading and MPV method is found to be not sensitive to G^Imax and ΔG^Ieff for displacement ratio of 0.1.

Mode I and Mode II fracture behavior in pultruded glass fiber-polymer – Experimental and numerical investigation

Many recent works have shown that the capacity of pultruded glass fiber-polymer structural members is governed by interlaminar failure. However, there is still a lack of information regarding the fracture properties associated and the best techniques to be adopted. This paper aims to propose a testing methodology and to evaluate the interlaminar fracture of pultruded glass fiber-polymer specimens extracted from a composite bridge deck system. Both Modes I and II were investigated, through Double Cantilever Beam (DCB) and End-Loaded-Split (ELS) tests, respectively. The starter crack (or initial separation) was introduced via a water jet machine and the crack length was measured with the video extensometer technique. In all, nine different methods were applied to obtain the fracture toughness properties. The results are discussed and compared with 2D non-linear finite element models, where the cohesive zone model (CZM) approach was used. The Modified Beam Theory method (MBTASTM) presented the best results for crack propagation in Mode I, whereas differences lower than 1% from experiments were obtained when using the Corrected beam theory using effective crack length (CBTE) and the Experimental compliance method (EMC) methods for Mode II.

The effective crack extension and its implications on the single cantilever beam test for sandwich composites

The response of Single Cantilever Beam sandwich specimens may be analyzed effectively through one-dimensional theories accounting for the actual deformation of the core and its effects on fracture parameters and compliance. The model of a beam on an elastic Winkler foundation describes the detaching facesheet as an Euler–Bernoulli beam resting, in the bonded region, on an elastic foundation which generates oscillating deflections with characteristic length [Formula: see text]. Modified beam theory (MBT) describes the debonded part of the face sheet as a cantilever beam, built-in at the debond tip, with an effective length which is longer than the actual detached length, by a quantity [Formula: see text]. If [Formula: see text] the two models predict the same energy release rate and similar load-point displacements. Effective crack extension and characteristic length depend on the thicknesses and elastic constants of facesheets and core and may be derived through experimental measurements of the specimen compliance at various increments of crack growth, as prescribed by experimental protocols. In the theoretical analyses, [Formula: see text] is typically assumed, either by directly using formulas proposed for other specimens or by calibrating their parameters to case specific finite element results. In this paper, we investigate the applicability of such formulas to a wide selection of sandwich composites for naval and aeronautical applications having thicknesses or materials other than those used for the original fitting; we then highlight their limitations and effects on the design of experimental protocols for material characterization. The applicability of a recent isotropic-elasticity based formula for [Formula: see text] is then verified using extensive data from the literature and novel finite element (FE) results for typical sandwich composites. Finally, a novel elasticity solution for the load-point displacement of a layer on a half plane is derived which supports the test data reduction procedure for [Formula: see text].

Investigation of the applicability of single cantilever beam test for the evaluation of fracture toughness of sandwich composites

Sandwich composites are widely used in load-carrying structures and there is a need for a testing method that will allow for qualitative and quantitative assessment of the bond between the facesheets and the core. The presented research investigates the applicability of the single cantilever beam (SCB) test to the evaluation of the mode I dominated fracture toughness of such structures under both quasi-static and fatigue loading.The SCB method uses a relatively simple fixture, the debond front loading conditions are independent of the debond length and the propagation takes place near the facesheet-to-core interface. It allows for the determination of the initiation and the propagation fracture toughness and can also be used for fatigue testing.A sandwich composite, made of carbon-epoxy facesheets and an aramid honeycomb core, was tested in quasi-static and fatigue loading conditions. The initiation values of the Energy Release Rate (ERR) were determined using the Modified Beam Theory (MBT) approach for different definitions of the initiation point. The propagation tests were conducted along with the visual observation of the debond growth. The propagation fracture toughness was determined using two approaches – MBT and the Area Method. The fatigue testing was realized, using the same setup, by cycling the specimens through a range of ERR values. The debond length was measured during the test which allowed for the determination of a relationship between the ERR and the debond length growth rate.The research confirmed that the SCB method can be used for the quantitative measurement of the fracture toughness of sandwich structures.

Experimental and Numerical Research of Delamination Process in CFRP Laminates with Bending-Twisting Elastic Couplings.

This paper aims at experimental and numerical research of delamination process in carbon/epoxy composite laminates with different fiber orientation angles in stacking sequence exhibiting the bending-twisting elastic couplings. Experimental specimens were subjected to the double cantilever beam (DCB) tests according to the ASTM D5528 regulations. Values of the mode I strain energy release rates were calculated by using three different data reduction schemes: the modified beam theory, the compliance calibration method and the modified compliance calibration. Determination of delamination initiation point was conducted in twofold way: by visual observation of crack tip using high resolution camera and by utilization of the acoustic emission technique. Numerical analyss were prepared in Abaqus/CAE Software environment by using the virtual crack closure technique (VCCT). The numerical beam model consisted of SC8R continuum shell elements. Obtained outcomes revealed that extensive fiber bridging phenomenon occurring during delamination process pronouncedly affected propagation values of strain energy release rate (GIprop) and numerically obtained load-displacement curves. Nevertheless, in initial stage of delamination, results obtained by using the VCCT were in agreement with experimental data. The greatest value of the mode I fracture toughness equal 0.56 N/mm was obtained for the BT45 laminate.

Mode I fracture behavior of unidirectional bamboo laminate and its applications to the estimation of bamboo-steel-bamboo connections’ bearing capacities

Fracture caused by crack propagation is prevalent in bamboo laminate. Mode I fracture of bamboo laminate in which the fracture surface is composed of multilayer strips with fracture along the Tangential-Longitudinal (T-L) direction was studied. The load-crack opening mouth displacement (CMOD) curves of Mode I fracture, and the post-peak behavior of bamboo laminate were analyzed. The Mode I fracture toughness was calculated based on the modified beam theory. The effect of the bamboo node on fracture toughness was studied. The Mode I fracture toughness of bamboo laminate increases with the crack growth due to bamboo nodes. The toughening mechanism is the interlocking effect and fiber bridging on the uneven fracture surface. The mean value of the Mode I fracture toughness of unidirectional bamboo laminate panels along the y-x direction of the unidirectional bamboo laminate was suggested to be 225.7 J/m2 for the estimation of bamboo-steel-bamboo connections' bearing capacities. Based on the measured fracture properties of bamboo laminate and the fracture mechanics models, the brittle bearing capacities of the bamboo-steel-bamboo connections were discussed at the end of this research.

On mechanical behavior of two-layer functionally graded sandwich curved beams resting on elastic foundations using an analytical solution and refined Timoshenko beam theory

For the first time, static bending, free vibration, and buckling studies of the two-layer functionally graded sandwich (TFGS) curved beams resting on Pasternak’s foundation utilizing the analytical precise solution and the refined Timoshenko beam theory (RTBT) are carried out in this study. The curved beam system is composed of two layers of single curved beams that are connected together by shear connectors. Each single curved beam layer is constructed entirely of FG sandwich material, including the bottom surface, core, and top surface. With the introduction of the new distribution shape function, it is possible to get a parabolic distribution of the transverse shear strain and shear stress throughout the whole thickness of the beam, with zero values at the beam's surfaces. The Navier solution is used to investigate the static bending, free vibration, and buckling of simply supported TFGS curved beams. The modified beam theory has been shown to be effective for analyzing the static bending, free vibration, and buckling responses of the beam system. The comparison of the deflection, normal and transverse shear stresses, natural frequency, and mechanical buckling load of curved beams computed using this proposed theory and other methodologies illustrates the new theory's correctness and effectiveness. Additionally, the influence of parameters such as the upper and lower layers' material volume exponents, the material ratio, the open angle, the thickness ratio, and the elastic foundation stiffness is explored. The study finding of this paper are really significant in terms of calculation and application in engineering practice. Contributing to the advancement of numerical computational mechanics by enhancing its development. Moreover, this is a critical and credible resource for future research on this sort of construction.

Fracture toughness and crack growth resistance of sandwich panels with grooved cores

The delamination phenomenon in sandwich panels occurs in the form of face/core debonding. The grooved foams are usually employed in curved sandwich structures for easier formability and better adhesion. In this research, the debonding toughness of facesheet to the core in a sandwich beam with grooved core is investigated using numerical and experimental methods. The sandwich beam consisted of two Kevlar 49/polyester facesheets and a polyurethane foam core. To obtain the values of strain energy release rate, the Cracked Sandwich Beam (CSB) specimen along with the Modified Beam Theory (MBT) method was used for the data reduction of the test results. In the numerical part, a model based on the cohesive zone theory was employed to simulate the crack growth in the specimens. Comparison of the numerical and experimental load–displacement curves indicated that the proposed model can reasonably predict the behavior of the structure under similar loading conditions. The effect of foam-related parameters such as the number and width of core grooves on crack growth resistance was examined numerically. The results showed that increasing the number and width of the grooves enhanced the resistance of the sandwich beams against the growth of interfacial cracks.

Debonding characteristics and strengthening mechanics of all-CFRP sandwich beams with interface-reinforced honeycomb cores

The weakest link in traditional sandwich beams constructed of carbon fiber reinforced polymer (CFRP) honeycomb core is arguably the bonded face sheet-core interface. This has limited the development and the expanded application of these sandwich structures. To overcome this, in this paper, a type of interface-reinforced honeycomb core is proposed to improve the bonding by enlarging the bonding area and thus increasing the strength of the face sheet-to-core attachment. A modified tailor-folding method is employed to fabricate two designs of the interface-reinforced honeycomb. The two interfaces reinforced cores are identical, except for the presence of machined holes in the strengthened fillet created to accommodate adhesive fillets formed during bonding. Double cantilever beam (DCB) test is performed to compare the bonding and behavior of the beams, which are tested alongside beams of a traditional honeycomb that is used as a control sample. In addition, the influences of cell wall thickness and loading direction with respect to the orientation of core macrostructures are also investigated. Modified Beam Theory (MBT) and Elastic Foundation Model (EFM) are employed to calculate the critical strain energy release rate. Overall, the interfaced-reinforced cores performed much better than the traditional core, with the former and latter being stronger in the transverse and longitudinal directions, respectively. The various failure modes observed from the test are analyzed and used to illustrate the strengthening mechanics operating in the interface-reinforced honeycomb.

Effect of moisture susceptibility and aging on interlaminar fracture behavior of fumed silica reinforced Jute‐Kevlar hybrid nanocomposite

AbstractThis work aims to examine the influence of moisture uptake of fumed silica reinforced Jute (J)‐Kevlar (K) hybrid composite on Mode I interlaminar fracture toughness. Mode I interlaminar fracture behavior is characterized by using the double cantilever beam (DCB) test specimen. Thirteen different composites are prepared based on four stacking sequences (i.e., Jute‐Jute‐Jute‐Jute [JJJJ], Jute‐Kevlar‐Kevlar‐Jute [JKKJ], Kevlar‐Jute‐Jute‐Kevlar [KJJK], and Kevlar‐Kevlar‐Kevlar‐Kevlar [KKKK]) and four nanofiller percentages (i.e., 0%, 1.5%, 3%, and 4.5%). Mode I fracture is experimented by using DCB test specimens. Mode I fracture energy (GIC) and Resistance curve (R‐curve) is evaluated by using the modified beam theory (MBT) data reduction method at dry and wet conditions of the specimens. The interlaminar fracture surface of the composites is analyzed using an optical microscope. It is noticed that moisture ingression severely affects the fiber bridging, which is a key factor influencing the Mode I fracture resistance. The presence of fumed silica also plays a vital role by preventing the microcracks generation surrounding the fibers due to fiber swelling. The fiber swelling is caused by moisture ingression. The composite with stacking sequence JKKJ and 3% of nanofiller (JKKJ‐3) is proved to be the reasonable Mode I fracture‐resistant material in moist environment.

Drag reduction of a blunt body through reconfiguration of rear flexible plates

We investigate the quasi-static reconfiguration of rear parallel flexible plates on the drag coefficient of a blunt body. The drag coefficient, plates deformation, and main features of the turbulent wake are characterized experimentally in a towing tank. It is found that increasing the flexibility of plates leads to an important drag reduction, induced by the progressive streamlining of the trailing edge due to plates deformation. The study of the Vogel exponent is adopted here to evaluate the limit on the potential drag reduction at large values of the Cauchy number, which is shown to be mainly caused by the growth in the vibrating amplitude response of plates. The plates deformation is analyzed by means of image processing, showing that their shapes mainly follow the first modal form of a cantilever beam deflection, although a slight concavity develops toward the plates tip for large Cauchy numbers. To further analyze this process, the empirical flow loading along the plates is estimated by a modified beam theory assuming a distributed load given by a power law. The experimental fitting shows that for large flexibility, the load diminishes at the rear tip. Besides, the progressive deformation of plates is shown to weaken the shedding of vortices and reduce the size of the recirculation bubble. Finally, an affine direct relationship between recirculation bubble aspect ratio and drag coefficient has been proposed in order to quantify the linkage between near wake modifications and hydrodynamic improvement provided by the trailing edge streamlining.

Upper and Lower Bounds for the Parameters of One-Dimensional Theories for Sandwich Fracture Specimens

AbstractUpper and lower bounds for the parameters of one-dimensional theories used in the analysis of sandwich fracture specimens are derived by matching the energy release rate with two-dimensional elasticity solutions. The theory of a beam on an elastic foundation and modified beam theory are considered. Bounds are derived analytically for foundation modulus and crack length correction in single cantilever beam (SCB) sandwich specimens and verified using accurate finite element results and experimental data from the literature. Foundation modulus and crack length correction depend on the elastic mismatch between face sheets and core and are independent of the core thickness if this is above a limit value, which also depends on the elastic mismatch. The results in this paper clarify conflicting results in the literature, explain the approximate solutions, and highlight their limitations. The bounds of the model parameters can be applied directly to specimens satisfying specific geometrical/material ratios, which are given in the paper, or used to support and validate numerical calculations and define asymptotic limits.

Parametric and non-parametric tests for the evaluation of interlaminar fracture toughness of polymer composites

This study is based on the statistical analysis of interlaminar fracture toughness of various laminated polymer composites used in aerospace applications through parametric and non-parametric tests. Tukey’s, Dunkan’s, two-sample t-test, and Kolmogorov–Smirnov tests are used to analyze tensile mode interlaminar fracture toughness of various fiber-reinforced polymer composites obtained by beam theory, modified beam theory, and modified compliance calibration method. Among the studied composite samples, modified compliance calibration method provided the highest average interlaminar fracture toughness, whereas the modified beam theory showed the lowest one. Room temperature cured carbon fiber-reinforced composite samples exhibited higher interlaminar fracture toughness than the autoclave cured samples. Two-sample t-test show that all methods are found coherent with each other in terms of being significantly different. On the contrary, Kolmogorov–Smirnov test revealed no significant difference. Besides, Tukey’s and Duncan’s tests exhibited almost the same results in regard to significant differences except those obtained by the modified compliance calibration method. Two-sample t-test method should have to be performed in order to observe significant relations rather than Kolmogorov–Smirnov test, since the results of Tukey’s and Duncan’s tests are only consistent with each other for the beam theory and modified beam theory method.

Experimental Investigation of Delamination in Composite Continuous Fiber-Reinforced Plastic Laminates with Elastic Couplings.

This paper presents an experimental evaluation of influence of the elastic couplings on the fracture toughness as well as on delamination initiation and propagation in carbon/epoxy composite laminates. For this purpose the mode I double cantilever beam (DCB) tests according to the American Society for Testing and Materials (ASTM) D5528 Standard were performed on specimens with different delamination interfaces and specific lay-ups composition exhibiting the bending-twisting (BT) and the bending-extension (BE) couplings. The critical strain energy release rates (mode I c-SERR, GIC) were calculated by using the classical methods, namely: the modified beam theory (MBT), the compliance calibration (CCM) and the modified compliance calibration (MCC). In order to evaluate an accuracy of the different methods, the values of c-SERR obtained by using standardized data reduction schemes were compared with values calculated by using the compliance based beam method (CBBM). All the methods give rise to comparable values of the GIC, which makes the CBBM an appealing choice, since it does not depend on crack length monitoring during the test. Initiation and propagation of delamination were investigated by using the acoustic emission (AE) technique. Moreover, the scanning electron microscope (SEM) analysis were performed after the experimental tests in order to investigate a fracture surface at delamination plane.

Mode-I interlaminar fracture behavior of laminated bamboo composites

Mode-I interlaminar fracture behavior of laminated bamboo composites was characterized by mechanical testing in a bonded double cantilever beam configuration. No obvious fiber bridging was observed during the test. At the front of crack tip, nonlinear response was relatively small and negligible. The failure mode of laminated bamboo composites was mainly governed by brittle fracture. Mode-I interlaminar fracture toughness ([Formula: see text]) calculated using the modified beam theory was 501.08 J/m2. Besides, numerical simulation combined with cohesive elements was used to simulate the mode-I interlaminar fracture behavior. A direct method for the determination of cohesive parameters without recourse to iterative fitting was presented in detail. The applicability and effectiveness of this method for interpretation of the fracture behavior of laminated bamboo composites were verified by comparing numerical predictions with experimental results.

Effect of intralaminar hybridization on mode I fracture toughness of natural fiber-reinforced composites

The main objective of this work was to investigate the effect of intralaminar hybridization on the mode I fracture toughness of epoxy composites based on jute and sisal fabrics. Four types of composites were produced by the hand layup technique: sisal (S), sisal + curaua (S + C), jute (J) and jute + curaua (J + C). Double cantilever beam (DCB) tests were performed, and the modified beam theory (MBT) method and three different data criteria (i.e. the deviation from linearity (NL), the 5% offset/maximum load (5%/Max) and visual observation (VIS)) were used to evaluate the mode I fracture toughness (GIc). It was found that the GIc of S + C and J + C composites increased by hybridization of pure sisal and jute fabrics and that the intralaminar hybridization limited the crack propagation. An X-ray microcomputed tomography (µCT) equipment was used to visualize the delamination and the form of the front of cracks inside the hybrid composites.

Study on mode-I fracture toughness of composite laminates with curved plies applied by automated fiber placement

Interlaminar fracture toughness is an important parameter to characterize the delamination performance of carbon fiber-reinforced epoxy laminates. In this study, the mode-I fracture toughness of interlaminar interfaces with different local ply angles were studied by experiments and numerical simulations. A set of double cantilever beam specimens of T800 carbon fiber/EH104 epoxy were prepared according to the ASTM-D5528–01 standard, where four specimens had straight ply interfaces (0°//0°, 15°//−15°, 30°//−30°, and 45°//−45°) and two specimens had curved ply interfaces (curvature radius: 300 and 500 mm). The mode-I fracture toughness was characterized using a data reduction scheme based on the modified beam theory. The results revealed that the mode-I fracture toughness values for the specimens with a curved ply interface were significantly higher than those for specimens with a straight ply interface.