Volcanic ash, a product of magma fragmentation, significantly impacts the environment and human society. The size, shape, and distribution of ash particles affect atmospheric dispersion and residence time. Magma fragmentation's explosivity depends on various factors including magma composition and eruption style, leading to diverse ash sizes and morphologies. Some ashes preserve pre-fragmentation bubbles, while others are bubble-free, particularly in low-intensity eruptions like Strombolian and Vulcanian eruptions which produce dense ash with few bubbles and finer ash than other eruptions. Magma, a viscous fluid, can fragment brittlely under rapid deformation relative to its relaxation time, characterized by the Deborah number (De). While a De > 0.01 threshold is generally accepted for brittle fragmentation, even within a viscous deformation regime (γ < 1/τr), solid-like fragmentation can be observed. This threshold is widely used in magma fragmentation models, though the rheology at fragmentation hasn't been directly measured. Existing models often focus on the brittle fragmentation of bubbly magma, where the product of overpressure and bubble volume fraction exceeds a critical value. However, this doesn't fully explain the formation of dense, bubble-poor ash. This research bridges the gap between the brittle fracture of magma (molten glass) above the glass transition temperature (Tg) and the well-studied fracture of amorphous materials below Tg, focusing on dissipative deformation (plastic/ductile/viscous) mechanisms, excluding low-viscosity processes driven by surface tension or inertia. The goal of this study is to investigate whether the complex fracture mechanisms observed in low-temperature glass also occur in high-temperature magma through tensile experiments on soda glass and haploandesite.

Extensive research explores magma fragmentation, focusing primarily on the brittle fracture of magma at high temperatures above the glass transition temperature (Tg). This contrasts with materials science studies on the fracture of amorphous materials below Tg, highlighting their plastic, ductile, and viscous characteristics. The fracture surfaces of glasses typically exhibit a tripartite morphology: mirror, mist, and hackle regions. The mirror region is smooth, the mist region is stippled, and the hackle region shows large undulations. The size of the mirror region is inversely proportional to tensile stress, and the rough mist and hackle regions arise from secondary crack formation and coalescence at the crack tip. Stress corrosion at the crack tip and the nucleation, growth, and coalescence of nanometric cavities are proposed mechanisms. However, the applicability of these low-temperature findings to high-temperature magmatic systems remains unclear. Studies on magma fragmentation often employ the Deborah number (De) to characterize the transition from viscous to brittle behavior, finding a threshold of De > 0.01. Other research utilizes rapid decompression experiments focusing on the role of pre-existing bubbles in initiating fragmentation, with smaller fragments forming at higher overpressures. But, these models do not adequately explain the formation of dense, bubble-poor ash produced in certain eruptions. This study addresses this gap by directly observing the fracture process at high temperatures and relating it to the material's rheological properties.

Tensile experiments were conducted using a custom-built apparatus (Fig. 1). Rod-shaped samples of soda glass and haploandesite were attached to an Inconel piston using spheres. The samples were heated in a vertical annular furnace, and the upper piston moved upward at various controlled strain rates. The force (load cell) and displacement (laser displacement sensor) were monitored to calculate stress and strain. High-speed cameras captured the fracture process in situ. The experimental conditions (temperature, strain rate, preheating temperature, sample dimensions) varied systematically (Table 1). The fracture surfaces were analyzed using scanning electron microscopy (SEM) and laser microscopy to characterize their morphology (smooth vs. rough regions). Rheological properties (viscosity and Young's modulus) were determined by fitting the measured stress-strain curves to a Maxwell fluid model (Eq. 2), taking into account the strain rate dependence of these parameters. The relaxation time (τ) was estimated using two methods: (1) the ratio of zero strain rate viscosity to infinite strain rate Young's modulus, and (2) from the strain-rate-dependent rheology data (Supplementary Fig. 3). This allowed for the calculation of the Deborah number (De) and assessment of whether fragmentation occurred in the viscous or elastic deformation regime. The composition of both soda glass and haploandesite samples are listed (Supplementary Table 1). The haploandesite was chosen for its magmatic similarity while being iron-free to ensure sample transparency and prevent crystallization during the experiment. Soda glass was selected because its room-temperature fracture behavior is well-documented, facilitating comparison with high-temperature results. Careful alignment of the sample and pistons was ensured to minimize stress components other than tension. Samples were prepared by melting and pulling up fibres, which were then cut into rods, and spheres attached for grip. The possible errors related to sample misalignment, non-uniformities in sample width due to preheating, and temperature estimation are discussed.

Experiments on molten soda glass at 630-660°C and haploandesite at 880°C revealed that fragmentation consistently generated small fragments, without necking. The fracture surfaces exhibited distinct smooth and rough areas, mirroring the morphology of room-temperature glass fractures (Figs. 2, 3, 5-7). The rough areas, originating from crack branching, were identified as the source of small fragments. Time scales of fracture were consistent with brittle fragmentation. Interestingly, stress-strain curves indicated that fragmentation generally occurred *after* the onset of viscous deformation, not solely within the elastic regime (Fig. 8). The maximum stress at fragmentation varied, yet normalized by the maximum viscous stress (3ηγ), most experiments fell around σmax/(3ηγ) ~ 1 (Fig. 8c), suggesting viscous deformation as the dominant factor triggering fragmentation. Strain rates did not decisively influence fragmentation, in contrast to the previously reported fragmentation threshold of γ̇τ > 0.01. This deviation can be potentially explained by the difference in experimental geometries (tensile vs. compressive/shear in the previous works) that changes the condition on stress concentration for crack initiation. The critical strain for fragmentation varied between materials and even within the same sample, potentially linked to the NBO/T ratio (non-bridging oxygen atoms per tetrahedrally coordinated cation), where higher NBO/T (less polymerization, as in the soda glass) requires less strain for fragmentation. Visual observations indicated brittle fracture, yet stress-strain curves suggested viscous deformation, thus the stress level at the fragmentation is not a determining factor.

The high-temperature fracture mechanism appears analogous to room-temperature glass fracture: cracks originate from flaws and propagate, with void nucleation causing instability and branching above a critical velocity, creating the rough surface. This interpretation agrees with recent molecular-scale strain observations. In natural magmas, bubbles and crystals act as nucleation sites, and volatiles can further influence crack propagation. Under high stress or strain rate, multiple cracks can initiate and branch, producing fine ash. Low stress and low vesicularity lead to viscous deformation, eventually culminating in fracture when conditions like reduced cross-sectional area or aligned bubbles/crystals are met. High vesicularity, with varied film thickness between bubbles, leads to easier fracture at low stress, forming pumices/scoriae, rather than generating abundant fine ash. The NBO/T ratio is a factor: lower NBO/T (higher polymerization as in haploandesite) may require greater strain for fragmentation, and the observation of deformed melt films in some silicic pumices might be connected to this. The formation of fine ash in eruptions like Strombolian and Vulcanian events may result from crack branching, whereas high vesicularity may result in lower stress level for fragmentation but not as much fine ashes (Fig.9).

This study demonstrates that high-temperature silicate melts can fragment in a manner similar to glass at room temperature, even under viscous deformation. The stress-strain curves showed that the fragmentation threshold isn't simply defined by a constant stress or strain but is strongly influenced by the onset of viscous deformation. Crack branching is proposed as the primary mechanism for generating fine, dense volcanic ash in low-vesicularity magmas. The NBO/T ratio of the melt is also suggested to be an important factor affecting the required strain for fragmentation. Further research should investigate the influence of various factors on the fragmentation process, including bubble size distribution, crystal content, and volatile composition, using combined experimental and numerical techniques.

The experiments were conducted under idealized conditions (homogeneous samples, controlled strain rate) which may not fully capture the complexity of natural magma fragmentation. The stress concentration at the sample-sphere interface might influence the fracture initiation. The simplified Maxwell fluid model used for rheological analysis might not fully account for the complex viscoelastic behavior of silicate melts under high stress and strain rates. Also, the direct application of our results to real magmatic systems should consider the effects of heterogeneous compositions, bubble distributions and crystalline phases, and volatile content which are not considered in our simplified experiments. More sophisticated numerical simulations and field observations are necessary to further refine and validate the proposed fragmentation mechanism.