Computational fracture modelling of polymer-bonded explosives and solid propellants: A critical review of local and nonlocal continuum formulations and discrete particle approaches

Inside the solid cores of rockets and the heavy charges of high explosives lies a material that looks like a dense, rocky cake but behaves like a complex, living tissue. These are polymer-bonded explosives and solid propellants, the workhorses of defense and aerospace. They are not uniform blocks of metal or simple plastics; they are crowded mixtures of hard, energetic crystals or oxidizer grains held together by a sticky, rubbery binder. This architecture is what makes them work, but it is also their greatest weakness. When these materials are subjected to the stress of storage, the shock of transport, or the heat of firing, the tiny gaps between the hard grains and the soft binder can open up. These microscopic separations, or debonding, can grow into cracks that compromise the structural integrity of the entire device. In the worst cases, the friction and heat generated by these cracks can trigger a premature explosion or a misfire. Because testing these materials is dangerous and often destroys the sample, scientists rely on computer models to predict how they will fail. However, the internal world of these materials is so messy and multi-layered that no single computer program has been able to capture the whole story, and while hybrid strategies offer a potential solution, their application to these materials remains at an early stage.

A team of researchers from China has conducted a comprehensive review of the various digital tools used to simulate this fracture process. They did not invent a new machine or run a single experiment; instead, they acted as cartographers, mapping out the strengths and weaknesses of five distinct computational approaches that scientists use to predict how these energetic materials break. The researchers examined methods that treat the material as a continuous solid, methods that focus on the specific surfaces where grains pull apart, and methods that break the material down into individual particles. By comparing how each tool handles the specific challenges of these crowded, crystal-filled mixtures, the team identified which approach is best suited for which specific type of failure, noting that the entries indicate mechanism-dependent tendencies rather than a universal ranking. Their work clarifies that there is no single "perfect" model. Instead, the choice of tool depends entirely on what the scientist is trying to predict: whether it is a single, sharp crack growing from a flaw, a widespread network of tiny separations, or the chaotic shattering of the material into fragments.

The first tool the researchers examined is a technique that allows a computer to draw a sharp crack through a grid of elements without having to redraw the grid every time the crack moves. This is useful when a material has a known weak spot, like a small hole or a pre-existing scratch, and the goal is to see how a single crack will travel from that point. The review found that this method works well for predicting the path of a dominant crack in a solid propellant grain or a specific explosive specimen. However, it struggles when the failure is not a single line but a scattered cloud of thousands of tiny breaks happening all at once. If the material is breaking apart in many places simultaneously, this method becomes too slow and cumbersome to be practical.

For situations where the failure happens along the boundaries between the hard grains and the soft binder, the researchers looked at a second approach that treats these interfaces like a special, breakable glue. This method is excellent for simulating the gradual peeling apart of the grains from the binder, a process known as dewetting, which is a common cause of failure in solid propellants. The computer can track exactly how much force is needed to pull the grains apart and how much energy is lost in the process. Yet, this method has a limitation: it requires the scientist to know exactly where the cracks will start. If the material fails in a way that was not pre-planned in the model, or if the cracks form inside the grains themselves rather than just at the edges, this tool cannot predict it.

When the failure is unpredictable, with cracks branching out in complex, tree-like patterns or appearing in many places at once, the researchers turned to a third method that replaces the sharp line of a crack with a fuzzy, spreading zone of damage. This approach is powerful because it does not need to be told where the crack will go; the computer figures it out based on the stress in the material. It is particularly good at showing how a single crack might split into two or how a network of cracks might merge together. However, the review noted that this method is computationally expensive, especially when trying to model the material in three dimensions. It also requires careful calibration to ensure that the "fuzziness" of the crack zone matches the actual physical size of the damage in the real material.

To handle the most violent scenarios, where the material shatters into many pieces and those pieces bounce and rub against each other, the researchers evaluated two more advanced techniques. One of these treats the material not as a solid block, but as a collection of points that interact with their neighbors over a short distance. This allows the material to break apart naturally without needing a special rule to tell it where to split. It is highly effective at simulating the rapid fragmentation seen in high-speed impacts. The other technique goes even further, modeling the material as a collection of individual, distinct particles that can move, rotate, and collide. This is the most detailed approach, capable of showing how the grains rearrange themselves after the binder fails. While this provides a very clear picture of the chaotic aftermath of a break, it is incredibly slow and requires massive computing power, making it difficult to use for large, real-world structures.

The central finding of the review is that the choice of method must be driven by the specific question being asked. If a scientist wants to know how a crack will grow from a known defect, a method that tracks sharp cracks is the right choice. If the goal is to understand how the grains separate from the binder, a method that focuses on interfaces is superior. If the material is expected to shatter into a cloud of debris, a method that treats the material as a collection of particles or a non-local network is necessary. The researchers emphasized that simply picking the most complex tool does not guarantee a better answer. In fact, using a tool that is too detailed for the problem can hide the true physics behind unnecessary complexity, while using a tool that is too simple can miss the critical failure mechanism entirely.

The review also highlighted a critical gap in current research: the difficulty of connecting the mechanical breaking of the material to the heat and chemical reactions that follow. When these energetic materials crack, the friction and deformation generate heat. If this heat gets trapped in a small spot, it can ignite the explosive. While some of the computer models can simulate the cracking and the heat generation separately, very few have successfully combined them to predict exactly when and where an ignition will occur. The researchers concluded that for these models to become truly reliable tools for safety, they must be tested against real-world data that was not used to build the models in the first place. They need to be able to predict how the material will behave in new situations, not just repeat what happened in the experiments used to tune them. Until these models can accurately predict the transition from a simple crack to a dangerous hot spot, they remain powerful simulations rather than perfect predictors.

Ultimately, the path forward lies in combining these different tools into hybrid systems. The researchers suggest that the best approach might be to use a simple, fast model for the parts of the material that are still intact, and then switch to a more detailed, particle-based model only in the specific areas where the material is breaking apart. This would allow scientists to capture the complex details of the fracture without overwhelming the computer. By matching the right digital tool to the right physical problem, and by rigorously testing these tools against independent experiments, the scientific community can move closer to a complete understanding of how these vital, yet fragile, materials behave under stress. This understanding is essential for designing safer, more reliable rockets and explosives that can withstand the harsh conditions of their service life without failing unexpectedly.