Composite wind turbine blades are typically reliable; however, premature failures are often in regions of manufacturing defects. While the use of damage modeling has increased with improved computational capabilities, they are often performed for worst-case scenarios in which damage or defects are replaced with notches or holes. To better understand and predict these effects, an effects-of-defects study has been undertaken. As a portion of this study, various progressive damage modeling approaches were investigated to determine if proven modeling capabilities could be adapted to predict damage progression of composite laminates with typical manufacturing flaws commonly found in wind turbine blades. Models were constructed to match the coupons from, and compare the results to, the characterization and material testing study presented as a companion. Modeling methods were chosen from established methodologies and included continuum damage models (linear elastic with Hashin failure criteria, user-defined failure criteria, nonlinear shear criteria), a discrete damage model (cohesive elements), and a combined damage model (nonlinear shear with cohesive elements). A systematic, combined qualitative–quantitative approach was used to compare consistency, accuracy, and predictive capability for each model to responses found experimentally. Results indicated that the Hashin and combined models were best able to predict material response to be within 10 % of the strain at peak stress and within 10 % of the peak stress. In both cases, the correlation was not as accurate as the wave shapes were changed in the model; correlation was still within 20 % in many cases. The other modeling approaches did not correlate well within the comparative framework. Overall, the results indicate that this combined approach may provide insight into blade performance with known defects when used in conjunction with a probabilistic flaw framework.
The Blade Reliability Collaborative (BRC), sponsored by the US Department of Energy and led by Sandia National Laboratories, has been tasked with developing a comprehensive understanding of wind turbine blade reliability (Paquette, 2012). A major component of this task is to characterize, understand, and predict the effects of manufacturing flaws commonly found in blades. Building upon coupon testing, outlined in the companion paper (Nelson et al., 2017), which determined material properties and characterized damage progression, three composite material defect types were investigated: porosity, in-plane (IP) waviness, and out-of-plane (OP) waviness. These defects were identified by an industry Delphi group as being common and deleterious to reliability (Paquette, 2012). Significant research into effects of common composite laminate defects has been performed for both porosity (Wisnom et al., 1996; Baley et al., 2004; Costa et al., 2005; Huang and Talreja, 2005; Pradeep et al., 2007; Zhu et al., 2009; Guo et al., 2009) and fiber waviness (Adams and Bell, 1995; Adams and Hyer, 1993; Cairns et al., 1999; Niu and Talreja, 1999; Avery et al., 2004; Wang et al., 2012; Lemanski et al., 2013; Mandell and Samborsky, 2013).
The goal of this portion of the overall project was to establish analytical approaches to model progressive damage in flawed composite laminates, consistently and accurately predicting laminate response. Multiple cases for each flaw type were tested, allowing for progressive damage quantification, material property definition, and development of many correlation points in this work. As outlined in the following sections, there have been two primary modeling approaches used to assess damage progression in composite laminates: continuum damage modeling (CDM) and discrete damage modeling (DDM). While these methods are well established, there has been little work directly assessing predictive capabilities when applied to wind turbine blade laminates with defects.
CDM is a “pseudo-representation” that does not explicitly model the exact
damage but instead updates the constitutive properties as damage occurs
(Kachanov, 1986). This allows for the relation of equations to heterogeneous
micro-processes that occur during strain of materials locally and during
strain of structures globally, insofar as they are to be described by global
continuum variables given their non-homogeneity (Talreja, 1985; Chaboche,
1995). Thus, for typical CDM as the model iterates at each strain level, the
constitutive matrix is updated to reflect equilibrium damage. Then as damage
occurs, the elastic properties are irreversibly affected in ways that are
similar to those in a general framework of an irreversible thermodynamic
process (Kachanov, 1986). This may take place by reducing the elastic
properties (
Empirical material properties utilized in progressive damage analysis.
There are two crucial considerations when modeling damage: the failure theory and ways to account for the damage. Typical failure criteria such as the maximum stress, the maximum strain, Hashin (1980), Tsai–Hill (1968), and Tsai–Wu (1971) are widely used because they are simple and easy to utilize (Christensen, 1997). In reviews by Daniel (2007) and Icardi (2007), wide variations in prediction using various theories were attributed to different methods of modeling the progressive failure process, the nonlinear behavior of matrix-dominated laminates, the inclusion or exclusion of curing residual stresses in the analysis, and the utilized definition of ultimate failure. Camanho and Matthews (1999) achieved reasonable experimental and analytical correlation using Hashin's failure theory to predict damage progression and strength in bearing, net-tension, and shear-out modes.
To account for damage, progressive damage models of composite structures range from the simple material property degradation methods (MPDMs) to more complex MPDMs that combine CDM and fracture mechanics (Tay et al., 2005a, b). Implementing a ply discount method whereby the entire set of stiffness properties of a ply is removed from consideration if the ply is deemed to have failed has been well established (Maimí et al., 2007). Typical examples of MPDM, which are directly compared to experimental findings (Blackketter et al., 1993; Gorbatikh et al., 2007), utilize a 2-D progressive damage model for laminates containing central holes subjected to in-plane tensile or compressive loading.
MPDM schemes are often implemented through user-defined subroutines (Chen et al., 1999; Xiao and Ishikawa, 2002; Goswami, 2005; McCarthy et al., 2005; Basu et al., 2007). Credited with being the first in this direction, Chang and Chang (1987) developed a composite laminate in tension with a circular hole where material properties were degraded to represent damage. Failure criteria were defined based on the failure mechanisms resulting from damage: matrix cracking, fiber–matrix shearing, and fiber breakage. A property reduction model was implemented and the results agreed for seven independent laminates. Later, Chang and Lessard (1991) performed similar work on damage tolerance of laminated composites in compression with a circular hole with similar results. These methods have been utilized for other conditions and have been used to develop a 3-D analysis methodology based on incorporating Hashin failure criteria into a similar logic (Evcil, 2008). By advancing to 3-D, the error dropped down to 2.6 % from as high as 30 %. Others have continually built upon these accumulation CDM approaches giving them breadth across a wide variety of composite material, loading, and structural applications (Camanho et al., 2007; Liu and Zheng, 2008; Sosa et al., 2012; Su et al., 2015).
In contrast, a DDM physically models the actual damage as it would physically occur through the load profile, typically as local failure of the constituents to be more consistent with the physical damage. With DDM approaches, constitutive properties do not physically change in a continuum sense; rather, the degradation is a consequence of a local failure as it would occur within a structure. In development of DDM approaches, knowledge a priori of the damage location is very helpful, though the result is that they are generally computationally more expensive.
While several different DDM methods exist (Rice, 1988; Moës and Belytschko, 2002; Krueger, 2004; Tay et al., 2005a), cohesive elements were chosen for this study due to the ability to control failure initiation. The Dugdale–Barenblatt cohesive zone approach may be related to Griffith's theory of fracture when the cohesive zone size is negligible compared with other characteristic dimensions (Dugdale, 1960; Barenblatt, 1962). The intent of the cohesive zone is to add an area of vanishing thickness ahead of the crack tip to more realistically describe the fracture process without the use of the stress singularity utilized in linear elastic fracture mechanics (Rice, 1988). Barenblatt (1962) theorized that a cohesive zone, which is much smaller that the crack length, exists near the crack tip and has a cohesive traction on the order of the theoretical strength of the solid. In addition, the parameters defining size of the zone and traction at onset are independent of crack size and extremal loads. Finally, no stress singularity exists because stresses are finite everywhere including at the crack tip. It is important to note that energy dissipation is an intrinsic mechanism of fracture with the cohesive approach in contrast to classic continuum fracture mechanics.
Zero-thickness elements are useful with laminated composites because they may be placed between layers or fibers. Cui and Wisnom (1993) used this type of element to predict delamination progression in specimens under three-point bending and in specimens with cut central plies. Duplicate nodes were used along the interface between distinct plies connected by two independent, zero-thickness springs, horizontal and vertical. As expected, the cohesive elements used showed a sudden discontinuous change in stiffness when the failure criterion was reached. The method was further developed by creating an element that provided a smoother transition from linear elastic behavior to plastic behavior (Wisnom et al., 1996; Petrossian and Wisnom, 1998). Later, a quasi-3-D model was proposed to predict, with reasonable results, both delamination and intra-ply damage prior to ultimate failure in a cross-ply laminate with a center crack loaded in tension (Wisnom and Chang, 2000). Planar elements were used on the surface of each ply and were then connected with nonlinear springs, as above, to model delamination between different plies. A similar technique was used to model longitudinal splitting along the fibers by means of spring interface elements across the line perpendicular to the notch where splitting is expected. A bilinear traction–separation criterion is commonly employed such that the element has a linear stiffness response until the maximum traction point is reached and damage is initiated (Turon et al., 2007). Then, the second portion of the bilinear response estimates the damage evolution up to failure at which separation occurs and the element is deleted. While the cohesion properties may successfully be calculated (Sørensen and Jacobsen, 2003; Turon et al., 2007), use of cohesive elements has also been successful where the bilinear response has been developed iteratively using experimental and analytical correlation (Tvergaard and Hutchinson, 1996; Allen and Searcy, 2001). While this method is computationally expensive due to the extensive number of elements needed, this method has been widely shown to effectively model crack propagation.
Representation of model and references used for the IP
Several different modeling approaches were utilized to most accurately model
the experimentation outlined in the testing companion paper (Nelson et al.,
2017). It is important for the reader to note that all references to material
testing and experimental results are from the work outlined in the companion
paper. For each modeling approach, the geometry was set up to match the
intended coupon size (100 mm
Several assumptions were made to simplify this modeling effort. First, it was assumed that all fibers were parallel and uniform in the intended direction with reference to the width-wise edge, including through the wave. It was also assumed that all the fibers, for both the unflawed and wave geometries, were parallel and aligned through the thickness. These assumptions greatly simplified the modeling approach even though they were a possible source of the variation noted within the testing. In addition, perfect bonding between the layers was assumed.
Damage initiation and evolution parameters utilized in progressive damage analysis.
The built-in Abaqus “Progressive Damage and Failure for Fiber-Reinforced
Materials” (Abaqus Software and Abaqus Documentation, 2012), which is
intended to be used for elastic-brittle, anisotropic materials based on the
Hashin failure criteria, was utilized. In this case, the elastic response is
defined as a linear elastic material with a plane stress orthotropic material
stiffness matrix. However, damage initiation must also be defined for the
four mechanisms included: fiber tension, fiber compression, matrix tension,
and matrix compression. Damage is initiated when one or more of these
mechanisms reaches a value of 1.0 or larger based on the material strengths
shown in Table 2:
Next, a user-defined subroutine was employed with a combined maximum stress–strain user-specified failure criterion for which the standard input file builds and meshes the model, while the user subroutine checks for damage at each step. If damage was detected, the material properties were adjusted as described in Table 3 or the loop was stopped if ultimate failure occurred. If damage but not ultimate failure was detected, the material properties were degraded depending on the type of failure, as outlined in Table 3 based on the three independent failure types: matrix cracking, fiber–matrix damage, and fiber failure. Based on the procedural logic from Chang and Chang (1987), an Abaqus code was written with a Fortran subroutine acting as the inner loop following the decision tree shown in Fig. 2 (Chang and Lessard, 1991).
Progressive damage analysis degradation for user-defined criteria.
Decision tree for progressive damage modeling utilized in this modeling.
To determine the failure values, both maximum stress and strain criteria
were implemented into the subroutine utilizing the material properties in
Table 1, the damage initiation values in Table 2, and a strain at failure of
2.6 %. If necessary, it was determined that the damage initiation
parameters could be modified within 10 % of the experimentally derived
values given the variations noted in the testing to improve correlation. A
modified maximum stress failure criterion was implemented with the inclusion
of a maximum strain criteria to accurately model ultimate matrix failure. As
such, matrix cracking damage was estimated using
A standard Abaqus code was written for an elastic material with three
dependencies to match the independent failure types before calling out a
Key points from empirical shear stress–strain relationship used in the nonlinear shear UMAT.
Thus, at each increment the subroutine ran through the failure criteria
equations that analyze the stress and strain data of that increment.
Resulting values of these equations range from 0 to 1 with failure occurring
when the value was equal to 1. As the failure indices were calculated to be
1, failure occurred in that element and the material properties were adjusted
based on the failure type as noted in Table 3. For example, if a matrix
failure occurred, the failure indices included in the user subroutine
calculated that the first failure value became equal to 1. Thus,
the elastic properties for that element only include
Based on the shear between the fiber tows in the wavy area, it was deemed
that a nonlinear constitutive law needed to be developed for the bulk
material by developing and using a user-defined material subroutine (UMAT) in
Abaqus Software and Abaqus Documentation (2012). As observed in the
experimental testing and indicated by Van Paepegem et al. (2006),
unrecoverable damage or plasticity occurs through the shear response. A
method to degrade the shear material properties based on the shear response
generalizing this damage and plasticity was implemented. Based on the change
in shear modulus during this degradation, eight points were identified where
changes in secant modulus were noted as identified in Fig. 3. Otherwise, all
material parameters were consistent with those listed in Table 1. The
tabulated shear stress–strain relationships (Fig. 3) were used to determine
the shear stress and tangential modulus using the subroutine once the stress
for the increment was calculated:
Once the shear stress and modulus were determined, the updates were returned into the material card of the model. It is important to note that since the tabulated shear points were identified as points at which the slope of the curve changed dramatically, correlation might be improved by taking other points so long as they were from the same data set. In other words, it was determined that the tabulated points could be changed to potentially improve correlation.
Representation of bilinear traction–separation response for a cohesive element.
Results of parametric studies to find the cohesive element:
To model damage progression discretely, cohesive elements are typically utilized based on a cohesive law relating traction to separation across the interface (Karayev et al., 2012; Lemanski et al., 2013). Zero-thickness elements with specific bilinear traction–separation criteria (Fig. 1a) were placed between the fiber tows of the material properties in Table 1 above. While following convention to utilize cohesive elements only in specific areas, computational availability has made it conceivable to place cohesive elements between all fiber tows throughout the model. Thus, damage and crack progression could occur between any fibers based on the stress state. It is important to note that the damage does not necessarily occur at the cohesive zone area. It only provides the opportunity for growth where damage can, and has been, experimentally determined to grow before final failure. Damage growth only occurs when and where the critical load is met. This is an important distinction from assuming a damage path as in the case of conventional linear elastic fracture mechanics.
A bilinear traction–separation criterion was implemented (Fig. 4) where the
initial stiffness,
The nonlinear shear CDM and the DDM using cohesive elements were combined due to their poor overall performance individually. As discussed below, in both cases, the models seemed to capture portion damage progression, while each lacked the exact progression observed in the testing. In this case, the methods described in Sect. 2.3 and 2.4 above were combined by adding the nonlinear shear routine to the cohesive zone model with the same material properties and parameters utilized from the material testing and parametric studies performed.
A systematic approach, as shown in Fig. 6, was employed to validate and compare different modeling methods. A qualitative–quantitative approach was utilized similar to that utilized by Lemanski et al. (2013), though strains at peak stress were also considered. The extensive test program found in the companion paper was used to validate this work both qualitatively and quantitatively (Nelson et al., 2017). As such, acceptable models correlated well both qualitatively, by matching failure location and shape, and quantitatively, by matching initial stiffness and peak stress at failure strain, to these experimental results. First, a qualitative assessment was performed and correlation was deemed acceptable if strain accumulation and damage progression visually matched the testing results. Using digital image correlation results from the material testing allowed for quick analysis of several key factors including an energy comparison. An energy comparison ensured that the energy was conserved between the strain energy available and energy dissipated. A visual comparison of the unrecoverable energy, or area under the curves, was deemed sufficient as models that do not conserve energy were evident and were not considered acceptable.
Systematic flow of approach to determine acceptability of each model.
If the qualitative criteria were met, a quantitative assessment was
performed. First, the strain at peak stress was compared and deemed
acceptable if it was within
Input parameters and acceptable parameters for modification with range of acceptable modification.
Tension and compression response of IP wave 1 utilized for baseline correlations with associated experimental variability.
As shown in Fig. 6, if correlation was not achieved by a model at any
point during the systematic increase in flaw complexity, the model was
deemed unacceptable and no additional flaw geometries were tested. The
increase in flaw complexity in each case progressed from unflawed controls
to porosity to the IP wave baseline case (Fig. 1a) to the initial OP
wave case (Fig. 1b), and then to other IP and OP geometries.
Acceptable models were able to accurately and consistently predict each of
these cases, and with this consistent systematic approach, the different
techniques were compared. The analytical models presented above were
created, run, and correlated to responses outlined in the testing effort and
modified, if necessary, to improve correlation if found to be outside the
The results from each model following the validation methodology are summarized in Table 5. These results are discussed through the progression of increasing complexity (unflawed, porosity, IP wave, OP wave, and additional waves) for each model. When compared to the experimental results, each model was scored based on the acceptance criteria with acceptable correlation (A), moderate correlation (M), and unacceptable correlation (U). There were several cases for which experimental results were not yet available due to complexity of testing (R). Also, once a method was deemed unacceptable, no additional models were run through the increasing complexity (NR). It should be noted that a modulus check (MC) on the unflawed specimen confirmed modulus correlation.
Summary of results of each model for acceptability.
Key: A: acceptable correlation (visual correlation and within 10 % of strain at peak stress & within 10 % of peak stress). M: moderate correlation (visual correlation but marginal quantitative acceptance criteria). U: unacceptable correlation (unacceptable visual and/or quantitative correlation). R: model run but not correlated (insufficient test data available). NR: model not run (due to unacceptable initial case or acceptable overall method). MC: initial modulus check (stiffness of model within 5 % of test).
For each modeling technique, a qualitative analysis, and then a quantitative analysis, was performed. The impetus of this was to ensure that the progressive damage models were consistent with the observed progressive damage in tests. The preliminary step for each model case was to ensure that the unflawed material response matched experimental results. Given the simplicity of the check, only a qualitative comparison of the initial modulus was made. In all cases, correlation was found to be within 5 %, as shown for a representative case in Fig. 8a. A similar result is noted for the 2 % porosity case correlation for the linear elastic with Hashin failure criteria (Fig. 8b). Given the good correlation between this method and the ease of use with the Kerner method of property reduction, no other modeling methods were examined for porosity. In short, this method was seen to meet the goal of an acceptable method of modeling this type of manufacturing defect found in wind turbine blades. Results in compression were similar for both cases but were only considered moderate for the porosity case due to large variation noted in the experimentation.
Correlation of analytical and experimental results for the
unflawed
Assessment of the correlations from modeling the initial IP wave case resulted in acceptance of the Hashin and combined methods but rejection of other methods (Table 5). A representative case comparing the as-tested IP wave with the combined model results at similar displacements is shown in Fig. 9. The qualitative comparison was performed by comparing the experimental images, taken from the data set shown with experimental stress–strain curve, at displacements of 0.5 and 2.0 mm with the model images generated at similar displacements. It is important to note, by identifying these displacements on the stress–strain curve, these snapshots along a similar progression. The reader is reminded that for the experimentation, full-field averages were used for strains (and for determining the material properties used); thus, a comparable approach was used for modeled strain, allowing for direct energy comparison. In Fig. 9 (left), it may be seen that failure occurred first at the edges where fibers were discontinuous at low loading, which matches the degradation noted in both stress–strain curves. As load increased, damage accumulation may be noted in the fiber misalignment section with shear failure occurring in the matrix as the fibers straightened due to tensile elongation (Fig. 9, right). As may be expected, the failure areas are cleaner and less complex for the models due to uniformity and symmetry of the modeled specimen. For this case, the qualitative correlation was quite consistent through the initial low-load portion of each analysis in which shear load increased significantly through the wavy section for all the modeling techniques.
Comparison of damage at displacements of approximately 0.5 and 2 mm between experimental (above) and analytical (below), showing onset to final damage from left to right, with points and damage progression identified on the resulting stress–strain curve.
The resulting stress–strain curves from each model are shown in Fig. 10.
While the Hashin failure criteria successfully met the acceptance criteria,
they did not exactly match the experimental material response, particularly
from 0.5–1.5 % strain in tension (Fig. 10). It is important to note that
while the damage initiation parameters were not modified, the damage
evolution parameters were modified to achieve the response shown. As noted in
the methods and Table 4 above, the initial damage evolution parameters were
approximated since they were not found experimentally. Given the acceptance
criteria outlined above, the predicted strain at peak stress was 1.35 %
compared to 1.53 % found experimentally or a variation of 12 %. As
such, these parameters were continually modified to 16
Resulting initial IP wave tension
In an unsuccessful attempt to offer the user more control to improve the modeling of the material response, the subroutine with user-defined failure criteria was used. As seen in Fig. 10, the results in tension did not match the acceptance criteria even after modification of the damage initiation parameters within the accepted 10 %. As seen in Fig. 10a, the damage initiation began at approximately 1 % strain at which the peak stress was achieved. To achieve correlation, the damage initiation parameters would become unrealistic based on the experimentation. As such, this approach was deemed unacceptable, as noted in modulus correlation. and no further attempts at correlation were made. However, it does capture the overall shape, and if degradation of the initial modulus due to early progressive failure can be justified based on experimental validations, it may warrant further work.
Resulting initial OP wave stress–strain curves of each model compared to experimental results.
While neither the nonlinear shear subroutine nor using cohesive elements independently could accurately model the experimentally observed response, areas of promise were identified in tension. The nonlinear shear response matched the experimental response up to failure more accurately than any other model (Fig. 10) up to approximately 1.4 % strain. At this point, the model showed that the wavy fibers had essentially straightened resulting in the increased stiffness indicated. Given that this was not seen experimentally, the approach was deemed unsuccessful. Similarly, when cohesive elements were placed between the fiber tows, matrix damage was modeled, though the peak stress and strain were both underpredicted. Since neither modeled the experimental damage progression, neither was used independently for additional cases (Table 5). Given these results, it was determined that adjusting the tabulated shear response or the traction–separation parameters would have no useful impact on the failures of each of these models.
However, based on the individual responses of these two techniques, a model was created placing cohesive elements between the fibers of the nonlinear shear subroutine model. When used to model the initial IP wave case, the response correlated to the experimental data without any modification of the acceptable parameters. It follows that no modification would be necessary given the experimental nature of the shear response and the proven methodology of parametrically finding the traction–separation parameters. Specifically, the combined model curve and experimental IP wave curve had similar responses up to 0.5 % strain as shown in Fig. 10. Above this point the model underpredicted the peak stress, which was attributed to the uniformity of the model, which was based on the average fiber misalignment angle. As such, the material failed through the thickness where all fibers were perfectly aligned, but the experimental specimens were not as consistent and some layers had a smaller fiber misalignment angle, which increased the load carrying capability. Regardless, the combined model was within the acceptable range and matched strain at failure where the cohesive failures caused the sudden drop in load-carrying capability. Based on this result, and the moderate correlation in compression (Fig. 10), additional correlations were attempted resulting in the best combination of accuracy, consistency, and predictive capability of all the modeling techniques tested (Table 5).
Resulting additional IP wave (16
Both the Hashin and combined models were run for the compression case (Fig. 11). Correlation was performed by comparing the full-field stress–strain data from the experimental to the model results. As noted, no changes were made to the input model parameters from the tension cases above except the use of the compression data in Table 1. Both models captured initial stiffness quite well up to approximately 1.5 % strain at which it is evident that the Hashin model was divergent, resulting in only moderately acceptable correlation. For the combined model, the first cohesive failures were noted at this strain, though load redistribution occurred and the model predicted the additional load carrying before additional cohesive failures. While the correlation was not perfect, it met the acceptance criteria.
To match the experimental work, additional waves were modeled at 16 and
48
For the combined case, similar initial stiffness results were noted in both
the 16
In summary, even though each model appeared to have different strengths, only the Hashin failure criteria and combined modeling techniques met the acceptable limits of the systematic approach employed. In both cases, this was true not only for the initial IP wave case but also for additional wave and material cases. Going forward, the combined model more accurately predicted both the initial stress–strain response and damage, even though the computational time was 5 times longer. It is important to note that improved correlation may be possible with the Hashin-based method given the approximations used for the damage evolution parameters. Since the combined approach was found to be the most accurate, consistent, and predictive, such validation of the Hashin-based method as implemented in Abaqus was not performed due to the need for constituent-level experimentation, which was beyond the scope of the work. Furthermore, while the Hashin model is adequate in a continuum mechanics sense, it does not physically represent the damage, which may be important in a damage-tolerant design approach for which damage inspections are necessary.
The application will dictate which approach, CDM or DDM, is most appropriate. If one only needs to know the global effects of local stiffness degradation due to damage, the CDM approach may be adequate. However, if one needs to know the actual damage, especially in a damage-tolerant design, certification, and operating environment, integrating DDM may be useful. To assess and predict the effects of manufacturing defects common to composite wind turbine blades, a comparison of several different damage progression models was performed resulting in several conclusions. Findings indicate that when material properties generated from unflawed material testing were used, all models were able to predict initial laminate stiffness when flaw geometries are discretely modeled. Models were run. and a systematic approach was followed to assess the results compared to experimental results of flawed specimens. Specifically, the CDM using Hashin failure criteria was found to be accurate, consistent, and predictive in tension for all wave and material cases once the damage properties were found. However, even though it accurately predicted the stress–strain response, it does not account for the actual, physical progressive damage observed during testing. To account for the variations noted and improve the accuracy, a user-defined failure criterion was run but results were not within the acceptable limits. Next, nonlinear shear UMAT and cohesive element approaches were independently developed and analyzed. While each independently captured portions of the response, both resulted in unrealistic responses. However, when these two methods were combined, the result was the most accurate, consistent, and predictive correlation. It is important to note the significance of Table 5, which is a succinct evaluation of what to expect from the various models and what needs to be improved for future work.
The results suggest that these analytical approaches may be used to predict material response to possibly reduce material testing and traditional scalar safety factors, while also potentially supporting a probabilistic reliability and certification framework. For this to be achieved, future work emphasizing scalability is necessary to be sure local defects are considered as part of the entire structure. This requires development of a multi-scale approach that requires an understanding of flaw response when surrounded by unflawed material. Appropriate modeling of this response will allow for a better understanding of flaws on larger structures.
Data may be found as reported to Sandia National
Laboratories
in Nelson et al. (2012a, b). In addition, data have also been added into
the
Blade Materials & Structures Testing Database compiled by the Composite
Technologies Research Group at Montana State University and the database is updated and
hosted by Sandia National,
The authors declare that they have no conflict of interest.
The authors wish to acknowledge the help from Sandia contract monitors Joshua Paquette and Daniel Laird. The authors also wish to acknowledge technical help from Tom Ashwill and Mark Rumsey. In addition, the work and research presented herein could not have been performed without the assistance of the entire Montana State University Composite Technologies Research Group. Edited by: Lars Pilgaard Mikkelsen Reviewed by: two anonymous referees