An experimental study of scaling effects in notched quasi-isotropic carbon/epoxy laminates under compressive loads
Introduction
Compressive strength of composite materials is of primary importance for designers. Budiansky and Fleck [1] considered compression as a critical case which needs to be understood. They reported that the typical failure mechanism for an unnotched unidirectional composite specimen under compression is by plastic kinking (local fibre micro-buckling). The kinking mechanism is sensitive to fibre misalignment which can occur during manufacturing, resulting in plastic shear deformation in the matrix when applying compressive loads. Wisnom [2] reviewed compression tests to investigate the variation in strength as the size of the unnotched specimen increases. The effects of manufacturing were highlighted. It was concluded that the scaling effect of compressive strength in composites is significant.
The reduction in the compressive strength due to the introduction of notches makes this a key driver when designing composite structures. Stress concentrations can arise from cut-outs, bolted joints or impact damage which can have detrimental effects on composite structures. There has been extensive research within this field to understand how scaling effects influence the compressive failure of open-hole composites. Bažant et al. [3] investigated unidirectional notched carbon–PEEK composites, failing by propagation of a kink band with fibre micro-buckling. They demonstrated that the strength scaling line for large notched specimens with a long kink band approaches an asymptote of slope −1/2 (characteristic of Linear Elastic Fracture Mechanics, LEFM) on the bi-logarithmic plot of the nominal strength vs. the characteristic size. Lee and Soutis [4] studied the failure mechanism of an open-hole quasi-isotropic specimen under compression while also investigating the size effects. They concluded that the failure was dominated by the presence of the hole, driving delamination and fibre micro-buckling along the plane of fracture in the vicinity of the hole. Wisnom et al. [5] summarised the strength scaling for sub-laminate scaled and ply-level scaled open-hole specimens under both tension and compression, demonstrating strong size effects under both loading conditions. Erçin et al. [6] also studied the effects of size on open-hole specimens under both tension and compression. They reported that the open-hole compressive strengths decrease faster than the open-hole tensile strengths with the same diameters ranging from 3 to 7 mm for a [90/45/0/−45]3s laminate. When comparing open-hole tension and compression test results, the open-hole tensile strengths were 66–91% higher than the open-hole compressive strengths with a greater difference for the largest specimens. Although no damage was observed prior to the peak load in the open-hole compression tests using Aramis Digital Image Correlation (DIC) system, sub-critical failure mechanisms were expected to have caused the size effect. The authors also applied Finite Fracture Mechanics models that have proven to be able to capture both the open-hole and centre-notched tensile and compressive failure [6]. However, the details of the sub-critical failure mechanisms under compression were not discussed. Few studies were found on compressive strength scaling for centre-notched quasi-isotropic laminates in the literature. Although Tan et al. [7] conducted experiments on relatively small quasi-isotropic specimens both with a sharp centre notch and an open hole under compression, no centre-notched or open-hole specimens of other sizes were tested. Furthermore, few studies compared the centre-notched failure under compression against the behaviour under tension.
Soutis et al. [8] developed a theoretical model to predict the notched strength of open-hole specimens and the critical micro-buckling length at failure. This model was derived from models [9], [10] originally developed for metals under tension, which were then modified for composites under compression. The micro-buckled region was modelled as a crack, over which the normal traction acting on the crack flanks was assumed to decrease linearly with the crack normal displacement. The correlation of the predicted open-hole results from the model and experimental results was very strong. This method has been integrated into a Composite Compressive Strength Modeller (CCSM) [11]. Other progressive damage modelling tools have been introduced to predict the strengths and failure patterns in open-hole specimens. For example, Su et al. [12] developed a progressive damage model for open-hole composite laminates under compression. They did not explicitly model the fibre micro-buckling, which was represented by a linear softening law instead. Under compression, instability and local buckling were problems that led to convergence issues. This was mitigated using a zigzagging softening curve developed by Ridha et al. [13], which always maintains a positive tangent modulus in the stress–strain curve. Pinho et al. [14] developed a smeared crack model, in which the total energy dissipated was proportional to the micro-buckling length propagation. The strain energy dissipated during the micro-buckling was mesh-independent as per the cohesive law embedded in this model. Ortega et al. [15] adopted an inverse approach to characterize the trans-laminar cohesive laws under both tensile and compressive loads. They compared different stacking sequences and materials, and highlighted the stress blunting effect of the blocked plies in the loading direction. They did not explicitly model the fibre micro-buckling either but derived a cohesive law to represent the micro-buckling process under compressive loads.
The present paper presents the scaling effect in centre-notched quasi-isotropic laminates under compressive loads. This was achieved by testing centre-notched specimens scaled in-plane by a factor of up to 14, with a constant notch-to-width ratio and laminate thickness. The Composite Compressive Strength Modeller (CCSM) [11] using the fracture toughness measured in the current study has been used to predict the scaling effects with satisfactory accuracy. Some further examinations were made to explain the development of the micro-buckling lengths, in which tests were interrupted at about 95% of the average failure load, and then X-ray Computed Tomography (CT scan) was conducted to analyse the internal damage prior to ultimate failure. For the first time centre-notched compression test results were compared to open-hole compression test results with the same material and specimen dimensions over a range of sizes. To form a full comparison, some very small and large open-hole specimens were also conducted in addition to the previous open-hole results from Lee and Soutis [4]. The failure mechanisms and scaling in both the open-hole and centre-notched compression tests were also compared with those in previous tension tests [16].
Section snippets
Specimen configurations
The schematic of all centre-notched specimen used is shown in Fig. 1, where W, L and C represents the specimen width, length and notch length respectively. The in-plane dimensions of the smaller specimens (C = 3.2, 6.35, 12.7 and 20 mm) are scaled as per Fig. 1a. The Scale 8 specimens (C = 25.4 mm) were tested with reduced gripping area as shown in Fig. 1b because of the limited width of the grips on the test machine. There is an even larger set of Scale 14 specimens (C = 45 mm) tested with no
Results summary
Table 2 presents the test results obtained for the notched specimens under compression for different specimen sizes. The strength values were taken as the gross-section stress from the load vs. displacement graph at ultimate failure. The displacements were measured at the crosshead. The load vs. crosshead displacement curves of the specimens of different sizes have a similar shape. There are no load drops until sudden failure as shown in Fig. 3a. The response is initially fairly linear until
Development of micro-buckling
The development of micro-buckling in the baseline, Scale 2, Scale 4 and Scale 8 specimens was examined by conducting CT scans of one specimen interrupted at 95% of the average failure load for each case. The purpose is to examine the damage state at the notch tip just before ultimate failure. Detailed information about fibre micro-buckling at the notch tip is the key to understanding notched compression failure.
Linear Elastic fracture Mechanics (LEFM)
In the current study, a trans-laminar fracture toughness KC = 43.9 MPa·m0.5 can be calculated from the largest Scale 14 centre-notched compression tests according to Eq. (1) [10].where ơn is the average nominal gross-section strength, from the largest Scale 14 compression tests, ơn_Scale14 = 161 MPa, and C = 45 mm is the crack length, is a geometric parameter to account for the effect of finite width and is the equivalent half notch-to-width ratio and W is the
Conclusions
The scaling effect of notched compressive strength in quasi-isotropic laminates was studied. The dominant failure mechanism under compression for both centre notches and open holes is fibre micro-buckling in the 0° plies initiating from the notch. CT scan images interrupted at about 95% of the average failure loads reveal that the fibre micro-buckling length is not a constant value but increases with notch length. The fibre micro-buckling does not grow parallel to the notch in the 0° plies, but
CRediT authorship contribution statement
Xiaodong Xu: Conceptualization, Methodology, Validation, Formal analysis, Investigation, Resources, Data curation, Writing - original draft, Writing - review & editing, Supervision, Project administration. Aakash Paul: Methodology, Software, Validation, Investigation, Resources, Writing - original draft. Xiaoyang Sun: Software, Validation, Investigation, Resources. Michael R. Wisnom: Conceptualization, Writing - review & editing, Supervision.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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